{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.dates as mdates\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "from sympy import Symbol, symbols, Matrix, sin, cos\n",
    "from sympy import init_printing\n",
    "from sympy.utilities.codegen import codegen\n",
    "init_printing(use_latex=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Extended Kalman Filter Implementation for Constant Turn Rate and Acceleration (CTRA) Vehicle Model in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Extended Kalman Filter Step](Extended-Kalman-Filter-Step.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Wikipedia](http://en.wikipedia.org/wiki/Extended_Kalman_filter) writes: In the extended Kalman filter, the state transition and observation models need not be linear functions of the state but may instead be differentiable functions.\n",
    "\n",
    "$\\boldsymbol{x}_{k} = g(\\boldsymbol{x}_{k-1}, \\boldsymbol{u}_{k-1}) + \\boldsymbol{w}_{k-1}$\n",
    "\n",
    "$\\boldsymbol{z}_{k} = h(\\boldsymbol{x}_{k}) + \\boldsymbol{v}_{k}$\n",
    "\n",
    "Where $w_k$ and $v_k$ are the process and observation noises which are both assumed to be zero mean Multivariate Gaussian noises with covariance matrix $Q$ and $R$ respectively.\n",
    "\n",
    "The function $g$ can be used to compute the predicted state from the previous estimate and similarly the function $h$ can be used to compute the predicted measurement from the predicted state. However, $g$ and $h$ cannot be applied to the covariance directly. Instead a matrix of partial derivatives (the Jacobian matrix) is computed.\n",
    "\n",
    "At each time step, the Jacobian is evaluated with current predicted states. These matrices can be used in the Kalman filter equations. This process essentially linearizes the non-linear function around the current estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Situation covered: You have a velocity sensor, which measures the vehicle speed ($v$) in heading direction ($\\psi$) and a yaw rate sensor ($\\dot \\psi$) which both have to fused with the position ($x$ & $y$) from a GPS sensor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State Vector - Constant Turn Rate and Acceleration Vehicle Model (CTRA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Constant Turn Rate, Constant Velocity Model for a vehicle ![CTRV Model](CTRV-Model.png)\n",
    "\n",
    "$$x_k= \\left[ \\matrix{ x \\\\ y \\\\ \\psi \\\\ v \\\\ \\dot\\psi \\\\ a} \\right] = \\left[ \\matrix{ \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Heading} \\\\ \\text{Velocity} \\\\ \\text{Yaw Rate} \\\\ \\text{longitudinal acceleration}} \\right]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "numstates=6 # States"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dt = 1.0/50.0 # Sample Rate of the Measurements is 50Hz\n",
    "dtGPS=1.0/10.0 # Sample Rate of GPS is 10Hz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All symbolic calculations are made with [Sympy](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-5-Sympy.ipynb). Thanks!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "vs, psis, dpsis, dts, xs, ys, lats, lons, axs = symbols('v \\psi \\dot\\psi T x y lat lon a')\n",
    "\n",
    "gs = Matrix([[xs+(vs/dpsis)*(sin(psis+dpsis*dts)-sin(psis))],\n",
    "             [ys+(vs/dpsis)*(-cos(psis+dpsis*dts)+cos(psis))],\n",
    "             [psis+dpsis*dts],\n",
    "             [axs*dts + vs],\n",
    "             [dpsis],\n",
    "             [axs]])\n",
    "state = Matrix([xs,ys,psis,vs,dpsis,axs])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamic Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This formulas calculate how the state is evolving from one to the next time step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6/OPl78DZFIpkCGtQHy3iMBZZOIpmVL+7fr+PEVFsYlQfwfIj+91FffMP/wiul8wkTN1d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\nQOChsOu7/wAxXo+zfCORxAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x + \\frac{v}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\y + \\frac{v}{\\dot\\psi} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\T \\dot\\psi + \\psi\\\\T a + v\\\\\\dot\\psi\\\\a\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡    v⋅(-sin(\\psi) + sin(T⋅\\dot\\psi + \\psi))⎤\n",
       "⎢x + ───────────────────────────────────────⎥\n",
       "⎢                    \\dot\\psi               ⎥\n",
       "⎢                                           ⎥\n",
       "⎢    v⋅(cos(\\psi) - cos(T⋅\\dot\\psi + \\psi)) ⎥\n",
       "⎢y + ────────────────────────────────────── ⎥\n",
       "⎢                   \\dot\\psi                ⎥\n",
       "⎢                                           ⎥\n",
       "⎢             T⋅\\dot\\psi + \\psi             ⎥\n",
       "⎢                                           ⎥\n",
       "⎢                  T⋅a + v                  ⎥\n",
       "⎢                                           ⎥\n",
       "⎢                 \\dot\\psi                  ⎥\n",
       "⎢                                           ⎥\n",
       "⎣                     a                     ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate the Jacobian of the Dynamic Matrix with respect to the state vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB4AAACWCAMAAAD+DcglAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x\\\\y\\\\\\psi\\\\v\\\\\\dot\\psi\\\\a\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡   x    ⎤\n",
       "⎢        ⎥\n",
       "⎢   y    ⎥\n",
       "⎢        ⎥\n",
       "⎢  \\psi  ⎥\n",
       "⎢        ⎥\n",
       "⎢   v    ⎥\n",
       "⎢        ⎥\n",
       "⎢\\dot\\psi⎥\n",
       "⎢        ⎥\n",
       "⎣   a    ⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Whh7qfVHon0DfQRBx3CbFzRHBm7FgOtO7D2WrKz1DBT+OvhBTrjaW6tuRmNXg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\nRK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & \\frac{v}{\\dot\\psi} \\left(- \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{1}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T v}{\\dot\\psi} \\cos{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{v}{\\dot\\psi^{2}} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & 0\\\\0 & 1 & \\frac{v}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{1}{\\dot\\psi} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T v}{\\dot\\psi} \\sin{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{v}{\\dot\\psi^{2}} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & 0\\\\0 & 0 & 1 & 0 & T & 0\\\\0 & 0 & 0 & 1 & 0 & T\\\\0 & 0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡      v⋅(-cos(\\psi) + cos(T⋅\\dot\\psi + \\psi))  -sin(\\psi) + sin(T⋅\\dot\\psi + \n",
       "⎢1  0  ───────────────────────────────────────  ──────────────────────────────\n",
       "⎢                      \\dot\\psi                               \\dot\\psi        \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢      v⋅(-sin(\\psi) + sin(T⋅\\dot\\psi + \\psi))  cos(\\psi) - cos(T⋅\\dot\\psi + \\\n",
       "⎢0  1  ───────────────────────────────────────  ──────────────────────────────\n",
       "⎢                      \\dot\\psi                              \\dot\\psi         \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0  0                     1                                      0            \n",
       "⎢                                                                             \n",
       "⎢0  0                     0                                      1            \n",
       "⎢                                                                             \n",
       "⎢0  0                     0                                      0            \n",
       "⎢                                                                             \n",
       "⎣0  0                     0                                      0            \n",
       "\n",
       "\\psi)  T⋅v⋅cos(T⋅\\dot\\psi + \\psi)   v⋅(-sin(\\psi) + sin(T⋅\\dot\\psi + \\psi))   \n",
       "─────  ────────────────────────── - ───────────────────────────────────────  0\n",
       "                \\dot\\psi                                   2                  \n",
       "                                                   \\dot\\psi                   \n",
       "                                                                              \n",
       "psi)   T⋅v⋅sin(T⋅\\dot\\psi + \\psi)   v⋅(cos(\\psi) - cos(T⋅\\dot\\psi + \\psi))    \n",
       "────   ────────────────────────── - ──────────────────────────────────────   0\n",
       "                \\dot\\psi                                  2                   \n",
       "                                                  \\dot\\psi                    \n",
       "                                                                              \n",
       "                                        T                                    0\n",
       "                                                                              \n",
       "                                        0                                    T\n",
       "                                                                              \n",
       "                                        1                                    0\n",
       "                                                                              \n",
       "                                        0                                    1\n",
       "\n",
       "⎤\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs.jacobian(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It has to be computed on every filter step because it consists of state variables!\n",
    "\n",
    "To Sympy Team: A `.to_python` and `.to_c` and `.to_matlab` whould be nice to generate code, like it already works with `print latex()`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initial Uncertainty $P_0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialized with $0$ means you are pretty sure where the vehicle starts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1000.,     0.,     0.,     0.,     0.,     0.],\n",
      "       [    0.,  1000.,     0.,     0.,     0.,     0.],\n",
      "       [    0.,     0.,  1000.,     0.,     0.,     0.],\n",
      "       [    0.,     0.,     0.,  1000.,     0.,     0.],\n",
      "       [    0.,     0.,     0.,     0.,  1000.,     0.],\n",
      "       [    0.,     0.,     0.,     0.,     0.,  1000.]]), (6, 6))\n"
     ]
    }
   ],
   "source": [
    "P = np.diag([1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0])\n",
    "print(P, P.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Process Noise Covariance Matrix Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"*The state uncertainty model models the disturbances which excite the linear system. Conceptually, it estimates how bad things can get when the system is run open loop for a given period of time.*\" - Kelly, A. (1994). A 3D state space formulation of a navigation Kalman filter for autonomous vehicles, (May). Retrieved from http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA282853"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[  3.09760000e-06,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   3.09760000e-06,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   4.00000000e-06,\n",
      "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          3.09760000e-02,   0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   4.00000000e-04,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00,   2.50000000e-01]]), (6, 6))\n"
     ]
    }
   ],
   "source": [
    "sGPS     = 0.5*8.8*dt**2  # assume 8.8m/s2 as maximum acceleration, forcing the vehicle\n",
    "sCourse  = 0.1*dt # assume 0.1rad/s as maximum turn rate for the vehicle\n",
    "sVelocity= 8.8*dt # assume 8.8m/s2 as maximum acceleration, forcing the vehicle\n",
    "sYaw     = 1.0*dt # assume 1.0rad/s2 as the maximum turn rate acceleration for the vehicle\n",
    "sAccel   = 0.5\n",
    "\n",
    "Q = np.diag([sGPS**2, sGPS**2, sCourse**2, sVelocity**2, sYaw**2, sAccel**2])\n",
    "print(Q, Q.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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QmpmVyCfDzMw6wEFrZlYyB62ZWckctGZmJXPQmpmVyCfDzMw6wEFrZlYyB62ZWckctGZm\nJev3oB3X7QLMzBqpnAwrcmtyvwdLukfSUkln1lj+Vkm/l/S8pDlVy5ZLul3SrZIWjXQs92jNrOe1\nu0craTxwEXAgsBJYKGl+RCzJrfYIcCpwRJ3d7BcR65o5nnu0ZtbzSujR7gksjYhlEfECcAUwK79C\nRKyJiIXAi6Otv+mglXSopJC0INe2b4O2G0dbnJkZtBS0kyUtyt1mV+1ye2BF7vHK1NasAK6TtLjG\nvjdSZOjgHek+Px4xVKOt1npmZi1rYehgXUQMjbxay/aJiFWSXg/8StLdEVG3c1lk6KBWgFbaFo+w\nnplZS0o6GbYK2CH3eGpqa0pErEr3a4CryYYi6hpt0Fb+Yiyu0eagNbO2KCFoFwIzJe0oaSJwNDC/\nyVo2k7R55WvgIOCORts0NXSQusdTgQciYnVq2wKYCTwUEStT2+bAm4HHgT/X2ddsYDbAtGnTmjm8\nmQ24ds86iIj1kk4BrgXGA5dGxJ2STkrL50ralqzDuAWwQdJngJ2BycDVqaZNgMsi4ppGx2t2jLZW\nL3UPQAzvze6e2m6JiKjzBOcB8wCGhoZqrmNmllfGGxYiYgGwoKptbu7rB8k6mNWeAN5W5FjNBu0e\n6f6WXFutYYPKOMXCIkWYmTXS7+8MazZoZ6b7+3JttU6EfTDd/2Y0RZmZVQzSZRInpPvJubZhwwmS\nDgL2JpuP9uu2VGdmRv/3aJuddXBzup8jaT9JWwI7AQ8BD0s6DrgS2ACcHBGjfieFmVlFGdc66KRm\ne7TfJhsWeC9wPfAk2Umv15ENDE8A7gWOj4iflVCnmQ2wXgzPIpoK2oh4XtL+wJHAh4ADgM2B1cA1\nZEMFP4mI9WUVamaDayCCFiAiNgBXAVdJ+jFwFHCqe7BmVqZeHQ4ootXLJPrdX2bWMQMXtJK2AnYE\nVkfEA+0vycxsuIELWtybNbMOG7igjYhfks04MDPriIELWjOzThrkk2FmZh3joDUzK5mD1sysZA5a\nM7OSOWjNzErkk2FmZh3goDUzK5mD1mwU7r///m6XUMj06dO7XcJActCamZXMQWtmViKfDDMz6wAH\nrZlZyRy0ZmYlc9CamZXMQWtmViKfDDMz6wAHrZlZyRy0ZmYlc9CamZXMQWtmViKfDDMz6wAHrZlZ\nyfo9aMd1uwAzs7HOPVoz63n93qN10JpZz3PQmpmVaCzMOig0Rivpw5JC0o0N1pkh6TlJj0raevQl\nmtmgq4Rts7deU7RH+8d0v0uDdc4HJgF/GxEPt1SVmVlOL4ZnEUWD9l7gaWArSdtFxOr8Qkl7A/8d\n+BNwYXtKNLNB1+9BW2joICI2ALenh7vmlyl7JS5ID+dExIu19iFptqRFkhatXbu2aL1mNoD6feig\nlXm0leGD3arajwH2Aq6LiJ/V2zgi5kXEUEQMTZkypYXDm9kgKRqyYy1oX+7RStoUOA94CTitDXWZ\nmb2sjKCVdLCkeyQtlXRmjeVvlfR7Sc9LmlNk22qtTO/aKGiB04FpwNyIuKOFfZqZ1dXuXqqk8cBF\nwIHASmChpPkRsSS32iPAqcARLWw7TCs92tuBAHaWNE7SNsCZwOPA2S3sz8ysoRJ6tHsCSyNiWUS8\nAFwBzMqvEBFrImIhUH2+acRtqxUO2oh4ElgGvBp4I/BFYHPgCxGxruj+zMxG0kLQTq6cdE+32VW7\n3B5YkXu8MrU1o/C2rb4z7I/ATsCxwCeBpcC3WtyXmVldLZ7gWhcRQ2XU04pWr95VGac9J+1jTupC\nm5m1XQlDB6uAHXKPp6a2UrYdbdCOB66PiJ+2uB8zsxGVELQLgZmSdpQ0ETgamN9kOYW3bWnoIAVr\n701WM7Mxqd2zDiJivaRTgGvJOoyXRsSdkk5Ky+dK2hZYBGwBbJD0GWDniHii1raNjuerd5lZzyvj\nTQgRsQBYUNU2N/f1g2TDAk1t24iD1sx6Wq++26sIB62Z9TwHrZlZyRy0ZmYlc9CamZXIY7RmZh3g\noDUzK5mD1sysZA5aM7OSOWjNzErkk2FmZh3goDUbhenTp3e7BOsDDlozs5I5aM3MSuagNTMrkU+G\nmZl1gIPWzKxkDlozs5I5aM3MSuagNTMrkU+GmZl1gIPWzKxkDlozs5I5aM3MSuagNTMr0Vg4GTZu\nNBtLOldSSDq3TfWYmW2kErbN3nqNe7Rm1vN6MTyLGG3QXghcAaxrQy1mZjUNdNBGxDocsmZWsoEO\nWjOzsvXquGsRDloz63n9HrRNzzqQdGiaYbAg17Zvg7Yb212smQ2mQZp18I50vyjXNlSjrdZ6L5M0\nG5gNMG3atAKHN7NB1YvhWUSRebS1ArTStniE9V4WEfMiYigihqZMmVLg8GY2qNyjzSyu0VYzaM3M\niujV8CyiqaCV9HpgKvBARKxObVsAM4GHImJlatsceDPwOPDnUio2s4EzEEFL7V7qHoAY3pvdPbXd\nEhEx+vLMzAYnaPdI97fk2moNG+yZ7heOpigzs7xBCdqZ6f6+XFutE2EfTPe/GU1RZmZ5gxK0E9L9\n5FzbsOEESQcBewMrgV+3pTozG3hj4WRYs9O7bk73cyTtJ2lLYCfgIeBhSccBVwIbgJMj4sX2l2pm\ng2pQpnd9m2xY4L3A9cCTZCe9Xgc8QdbjvRc4PiJ+VkKdZjbAejE8i2iqRxsRzwP7Ax8GLgeeS4tW\nA98DjgLe6pA1szKU0aOVdLCkeyQtlXRmjeWS9M20/DZJe+SWLZd0u6RbJY34noGm37AQERuAq4Cr\nJP2YLFxPdbiaWdna3aOVNB64CDiQ7LzSQknzI2JJbrVDyCYCzAT2Ai5J9xX7pUvFjqjVj7Lxu7/M\nrCOK9mabDOU9gaURsSwiXiD7AINZVevMAn4YmZuBLSW9oZXnUDhoJW0F7AisjogHWjmomVkRLQTt\nZEmLcrfZVbvcHliRe7wytTW7TgDXSVpcY98baeV6tO7NmllHtTB0sC4ihkZerWX7RMSqdHmCX0m6\nOyLqXhq2cNBGxC/JZhyYmXVECbMOVgE75B5PTW1NrRMRlfs1kq4mG4qoG7Sj+rhxM7NOKGGMdiEw\nU9KOkiYCRwPzq9aZDxyfZh+8C3g8Ih6QtFm6gBaSNgMOAu5odDB/lI2Z9bQy3oQQEeslnQJcC4wH\nLo2IOyWdlJbPBRYAhwJLgWeAT6TNtwGuTjVtAlwWEdc0Op6D1sx6XhlvWIiIBWRhmm+bm/s6gJNr\nbLcMeFuRYzlozazn9fs7wxy0ZtbzHLRmZiVz0JpZT+r3cKro1StyFeGgNbOe56A1MyuZg9bMrGQO\nWjOzkjlozcxK5JNhZmYd4KA1MyuZg9bMrGQOWjOzkjlozcxK5JNhZmYd4KA1MyuZg9bMrGQOWjOz\nkjlozcxK5JNhZmYd4KA1MyuZg9bMrGT9HrTjWt1Q0s6SzpF0g6T7JT0v6XFJN0k6pp1Fmtlgq4zT\nNnvrNaPp0X4dOABYAtwO3AzMBPYB9pG0dURcOPoSzWyQ9Wp4FjGaoP02cFxErM03Sjoc+ClwBuCg\nNbNRG9igjYir67TPl7QWmCppXERsyC+XNBuYDTBt2rRWD29mA2Rgg1bSRGB/4J3AG4BXAZVXYzLw\nWHXIAkTEPGAewNDQULR6fDMbHAMZtJKOBi4Atm2w2pKWKjIzq9LvQVt41oGkY4HLgYnA54C3A68F\nxkeEgM+mVRe3q0gzG1xFZxz0Yii30qP9Uro/JCL+UGP5x9K9g9bM2qIXw7OIQkEr6bXADOD5WiEr\n6Xhg9/Rw0airMzOj/4O26NDBk8BTwCRJB+cXpHHbuenh08Ddoy/PzKz/37BQKGjTLIKL0sOfS/ql\npMsl3Q18H7g4Lbs1Il5qY51mNqAGdYz2LOBR4ARgX+Ah4JfAfwU+kNbx+KyZtU0vhmcRhYM2ItYD\n56dbtYt5pVdrZtYWAxe0Zmad5qA1MyuZg9bMrES9eoKrCAetmfU8B62ZWckctGZmJev3oG35o2zM\nzKw57tGaWc9zj9bMrERlvQVX0sGS7pG0VNKZNZZL0jfT8tsk7dHsttUctGbW89odtJLGk1235RBg\nZ+AYSTtXrXYI2QfOziT7+K1LCmw7jIPWzHpeCT3aPYGlEbEsIl4ArgBmVa0zC/hhZG4GtpT0hia3\nHaarY7SLFy9eJ+n+EnY9GVhXwn7L4FrL4VrLUUat0xstXLx48bXjxo2bXHCfm0rKXxN7Xvq8wort\ngRW5xyuBvar2UWud7ZvcdpiuBm1ETCljv5IWRcRQGftuN9daDtdajm7UGhEHj7xWb/OsAzMbRKuA\nHXKPp6a2ZtaZ0MS2w3iM1swG0UJgpqQdJU0EjgbmV60zHzg+zT54F/B4RDzQ5LbDjNUe7byRV+kZ\nrrUcrrUc/VRrXRGxXtIpwLXAeODSiLhT0klp+VxgAXAosBR4BvhEo20bHU8RUdqTMTMzDx2YmZXO\nQWtmVjIHrZlZyRy0ZmYlc9B2iKTDJIWkmxus8xZJz0laLWmLTtZXVcehqdYFubZ9G7Td2J1K+5+k\nc9NreG63a7HyOGg757dAALtL2rTOOpcAk4DTIuKJjlW2sXek+/xbGIdqtNVaz8yq9H3QSvpS6hFc\nV2OZJP2o0hOTNKEbNQJExCPAncBEXgmtl0k6HtgPuDYiruxwedVqBWilbfEI63WUpA+P1KuWNCP9\np/CopK07WV8TLgT+It33JEk7SzpH0g2S7pf0vKTHJd0k6Zhu19cXIqKvb8AWwBqy3uIBVcsuTO3/\nBryqB2q9ONXzv6rat0rP4Vlgpx6oc0Wqc7tc2z2pbWqu7e7U9uYu1joz1fBwg3WuTOuc1u3Xth9v\nwDXAeuA24Ofp9bwlvaYBnNLtGnv91vUC2vSD8On0DV+Ya/t8alsEbNHtGlNNR6earq5q/25qP7sH\nanx9qmV1rm0LYAPwYK5t89T2GOmNL12qdxzwVPUfhtzyvdOye4AJ3X59+/EGHAlMqdF+eHptV3S7\nxl6/9f3QQTKPrHc1lP6V/BvgbOAu4ODo7nhn3k3pfu9Kg6R9gE+SBcH53SiqSq2x2D0AMXzYYPfU\ndkuk37puiIgNwO3p4a75ZcouTHpBejgnIl7sZG1jRURcHRFra7TPB9YCUyWNlSwpxZh4cSJiPXBG\nengJ2S/XcuDAiOiZ63xGxCrgPmAbSW9MY8ZzyQLr05FdRLjbKh/XcUuurRK++aDdM90vLL2ikf0x\n3e9W1X4M2XVCr4uIn3W2pI3162wOSRPTR7ecLeliSd+X9ANJPyC7Pu1j6Q+e1TFmLioTEfMlLSH7\naIk1ZOO1DS9d1iU3AjsC7ya71NouwI8i4vquVvWKmen+vlxbrRNhH0z3vym9opFVgvblHm2a2XEe\n8BJwWjeKqqHvZnNIOpqs47Jtg9WWdKicvjUmerQAkk4lC1mATYFeGS6oVhk+OJZseOMx4PTulbOR\nysyM/BXth4WBpIPIhj9WAr/uXGl1bRS0ZK/pNOA7EXFH50uqqW9mcwBIOha4nGymzOeAtwOvBcZH\nhIDPplUX196Dvazbg8TtuAEfJzsxs5LsupABXNjtuurU+mZeOVsbwEndrqmqvlNTXQ+QTTfbMr22\nD5L9ATsOeJSsp3h4t+tNNVdOzD1N1nnYhuwP7WPA5G7Xl6uzb2ZzpDruS3XsWWd5ZebBx7v92vb6\nresFtOGH4UiyqSfryOYj7kA2TerFbv+gNqj5wfQDejMwrtv1VNU2Cbgh94fgiXT/PPBC+nopcFi3\na62qe2mq7U3Ad9LXn+12Xbn6+m02x2tTvc/VWX587mdkl26/vr1+6+uhA0kHkP1r8wzZ7IK7ImIF\n2fzZTYAvd7O+WiS9Jn35EllvtqdOIkTE88D+wIfJXtvn0qLVwPeAo4C3Rg+cXKpSGT44lmwWx1Lg\nW90rZyN9NZsDeJJs2twkScM+syuN285ND58m64FbA30btOmjJX6SHs6KiPwP8HnA48CRkt7T8eIa\nO5vsX9tvRsSt3S6mlojYEBFXRcSxZL1bgFMj4lMR8c+RzfLoNZWgPYfs53pO9MYsjoq+ms2ROgAX\npYc/l/RLSZdLuhv4PtmbbwBujYiXulJkH+nLoJW0G9nHTEwCPhIRw858R/Z218qc1K92uLy6JO1P\ndpJmGVnb/3IwAAABRElEQVTg9oNaPbFeVAna8cD1EfHTbhZTQz/O5jgLOJPs53VfspkyN5GddFyW\n1vGJsCb4o2xKJmkXsulF2wIfIBs73reqB96TJG0FPEw2rrh9t+vpZ5IuI5vXOycivpba/kw2pjw1\nIlal2RzXkp3UfWP4DRZjRl/2aPvMB4ATyHoEN5G9iaLnQzbpl95sP6hcHnOOpP0kbQnsBDwEPCzp\nOLJrCGwATnbIji3u0Zp1gKRJZL3V96amJ8lmGLxAdvJrAnAv2YVveu1Eo42Sg9asQ9L1AI4EPgQc\nAEwhe6v4NWRv/PhJj55otFFy0Jp1gaQfk02VO9w92LHPY7Rm3eHx7wHiHq1Zh3k2x+Bxj9as89yb\nHTDu0ZqZlcw9WjOzkjlozcxK5qA1MyuZg9bMrGQOWjOzkjlozcxK5qA1MyuZg9bMrGT/HyQpEgRw\ngo8NAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1169cf310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "im = plt.imshow(Q, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Process Noise Covariance Matrix $Q$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(9))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(8),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$', '$a$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(9))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(8),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$', '$a$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,5.5])\n",
    "plt.ylim([5.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Real Measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Read '2014-03-26-000-Data.csv' successfully.\n"
     ]
    }
   ],
   "source": [
    "#path = './../RaspberryPi-CarPC/TinkerDataLogger/DataLogs/2014/'\n",
    "datafile = '2014-03-26-000-Data.csv'\n",
    "\n",
    "date, \\\n",
    "time, \\\n",
    "millis, \\\n",
    "ax, \\\n",
    "ay, \\\n",
    "az, \\\n",
    "rollrate, \\\n",
    "pitchrate, \\\n",
    "yawrate, \\\n",
    "roll, \\\n",
    "pitch, \\\n",
    "yaw, \\\n",
    "speed, \\\n",
    "course, \\\n",
    "latitude, \\\n",
    "longitude, \\\n",
    "altitude, \\\n",
    "pdop, \\\n",
    "hdop, \\\n",
    "vdop, \\\n",
    "epe, \\\n",
    "fix, \\\n",
    "satellites_view, \\\n",
    "satellites_used, \\\n",
    "temp = np.loadtxt(datafile, delimiter=',', unpack=True, \n",
    "                  converters={1: mdates.strpdate2num('%H%M%S%f'),\n",
    "                              0: mdates.strpdate2num('%y%m%d')},\n",
    "                  skiprows=1)\n",
    "\n",
    "print('Read \\'%s\\' successfully.' % datafile)\n",
    "\n",
    "# A course of 0° means the Car is traveling north bound\n",
    "# and 90° means it is traveling east bound.\n",
    "# In the Calculation following, East is Zero and North is 90°\n",
    "# We need an offset.\n",
    "course =(-course+90.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurement Function H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix $J_H$ is the Jacobian of the Measurement function $h$ with respect to the state. Function $h$ can be used to compute the predicted measurement from the predicted state.\n",
    "\n",
    "If a GPS measurement is available, the following function maps the state to the measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB4AAAB9CAMAAACCjiNkAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x\\\\y\\\\v\\\\\\dot\\psi\\\\a\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡   x    ⎤\n",
       "⎢        ⎥\n",
       "⎢   y    ⎥\n",
       "⎢        ⎥\n",
       "⎢   v    ⎥\n",
       "⎢        ⎥\n",
       "⎢\\dot\\psi⎥\n",
       "⎢        ⎥\n",
       "⎣   a    ⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hs = Matrix([[xs],\n",
    "             [ys],\n",
    "             [vs],\n",
    "             [dpsis],\n",
    "             [axs]])\n",
    "hs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALYAAAB9CAMAAAA4AWlBAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\n7gcMX3EdcFYrywAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 1 & 0 & 0\\\\0 & 0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  0  0  0  0  0⎤\n",
       "⎢                ⎥\n",
       "⎢0  1  0  0  0  0⎥\n",
       "⎢                ⎥\n",
       "⎢0  0  0  1  0  0⎥\n",
       "⎢                ⎥\n",
       "⎢0  0  0  0  1  0⎥\n",
       "⎢                ⎥\n",
       "⎣0  0  0  0  0  1⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JHs=hs.jacobian(state)\n",
    "JHs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If no GPS measurement is available, simply set the corresponding values in $J_h$ to zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurement Noise Covariance $R$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"In practical use, the uncertainty estimates take on the significance of relative weights of state estimates and measurements. So it is not so much important that uncertainty is absolutely correct as it is that it be relatively consistent across all models\" - Kelly, A. (1994). A 3D state space formulation of a navigation Kalman filter for autonomous vehicles, (May). Retrieved from http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA282853"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[  2.50000000e+01,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   2.50000000e+01,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   9.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          1.00000000e-02,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   1.00000000e+00]]), (5, 5))\n"
     ]
    }
   ],
   "source": [
    "varGPS = 5.0 # Standard Deviation of GPS Measurement\n",
    "varspeed = 3.0 # Variance of the speed measurement\n",
    "varyaw = 0.1 # Variance of the yawrate measurement\n",
    "varacc = 1.0 # Variance of the longitudinal Acceleration\n",
    "R = np.diag([varGPS**2, varGPS**2, varspeed**2, varyaw**2, varacc**2])\n",
    "\n",
    "print(R, R.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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r/ebbrBKzvxjYFtgFWAR8pUxNbqmZWWVdtNSWRsS0buYdEYsLr/Nt4Ooyz3OomVklo31E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\noWZmjeJQM7NGcaiZWaM41MysUf4/1ql37macuXgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11698f990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(4.5, 4.5))\n",
    "im = plt.imshow(R, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Measurement Noise Covariance Matrix $R$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(5),('$x$', '$y$', '$v$', '$\\dot \\psi$', '$a$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(5),('$x$', '$y$', '$v$', '$\\dot \\psi$', '$a$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,4.5])\n",
    "plt.ylim([4.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Identity Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1.,  0.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  1.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  1.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  1.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  1.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  0.,  1.]]), (6, 6))\n"
     ]
    }
   ],
   "source": [
    "I = np.eye(numstates)\n",
    "print(I, I.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approx. Lat/Lon to Meters to check Location"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RadiusEarth = 6378388.0 # m\n",
    "arc= 2.0*np.pi*(RadiusEarth+altitude)/360.0 # m/°\n",
    "\n",
    "dx = arc * np.cos(latitude*np.pi/180.0) * np.hstack((0.0, np.diff(longitude))) # in m\n",
    "dy = arc * np.hstack((0.0, np.diff(latitude))) # in m\n",
    "\n",
    "mx = np.cumsum(dx)\n",
    "my = np.cumsum(dy)\n",
    "\n",
    "ds = np.sqrt(dx**2+dy**2)\n",
    "\n",
    "GPS=(ds!=0.0).astype('bool') # GPS Trigger for Kalman Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initial State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 0.        ],\n",
      "        [ 0.        ],\n",
      "        [-4.08756111],\n",
      "        [ 0.67322222],\n",
      "        [-0.32660346],\n",
      "        [ 0.2647    ]]), (6, 1))\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwsAAAAUBAMAAAAw4LxaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\npimWTrUAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left ( -0.00180704898447, \\quad 0.00180704898447, \\quad -0.00278237674761, \\quad 0.00278237674761\\right )$$"
      ],
      "text/plain": [
       "(-0.00180704898447, 0.00180704898447, -0.00278237674761, 0.00278237674761)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NLAxJUhMLQ5LUxMKQJDWxMCRJTSwMSVITC0OS1MTCkCQ1sTAkSU0sDElSEwtDktTEwpAk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\nSWpiYUiSmlgYkqQmFoYkqYmFIUlq8v8AnjojL1r99JQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1169c1f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.matrix([[mx[0], my[0], course[0]/180.0*np.pi, speed[0]/3.6+0.001, yawrate[0]/180.0*np.pi, ax[0]]]).T\n",
    "print(x, x.shape)\n",
    "\n",
    "U=float(np.cos(x[2])*x[3])\n",
    "V=float(np.sin(x[2])*x[3])\n",
    "\n",
    "plt.quiver(x[0], x[1], U, V)\n",
    "plt.scatter(float(x[0]), float(x[1]), s=100)\n",
    "plt.title('Initial Location')\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Put everything together as a measurement vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5, 10800)\n"
     ]
    }
   ],
   "source": [
    "measurements = np.vstack((mx, my, speed/3.6, yawrate/180.0*np.pi, ax))\n",
    "# Lenth of the measurement\n",
    "m = measurements.shape[1]\n",
    "print(measurements.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Preallocation for Plotting\n",
    "x0 = []\n",
    "x1 = []\n",
    "x2 = []\n",
    "x3 = []\n",
    "x4 = []\n",
    "x5 = []\n",
    "x6 = []\n",
    "Zx = []\n",
    "Zy = []\n",
    "Px = []\n",
    "Py = []\n",
    "Pdx= []\n",
    "Pdy= []\n",
    "Pddx=[]\n",
    "Pddy=[]\n",
    "Pdv =[]\n",
    "Kx = []\n",
    "Ky = []\n",
    "Kdx= []\n",
    "Kdy= []\n",
    "Kddx=[]\n",
    "Kdv= []\n",
    "dstate=[]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Extended Kalman Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Extended Kalman Filter Step](Extended-Kalman-Filter-Step.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$x_k= \\begin{bmatrix} x \\\\ y \\\\ \\psi \\\\ v \\\\ \\dot\\psi \\\\ a \\end{bmatrix} = \\begin{bmatrix} \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Heading} \\\\ \\text{Velocity} \\\\ \\text{Yaw Rate} \\\\ \\text{acceleration} \\end{bmatrix} =  \\underbrace{\\begin{matrix}x[0] \\\\ x[1] \\\\ x[2] \\\\ x[3] \\\\ x[4] \\\\ x[5]  \\end{matrix}}_{\\textrm{Python Nomenclature}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for filterstep in range(m):\n",
    "\n",
    "    # Time Update (Prediction)\n",
    "    # ========================\n",
    "    # Project the state ahead\n",
    "    # see \"Dynamic Matrix\"\n",
    "    if np.abs(yawrate[filterstep])<0.0001: # Driving straight\n",
    "        x[0] = x[0] + x[3]*dt * np.cos(x[2])\n",
    "        x[1] = x[1] + x[3]*dt * np.sin(x[2])\n",
    "        x[2] = x[2]\n",
    "        x[3] = x[3] + x[5]*dt\n",
    "        x[4] = 0.0000001 # avoid numerical issues in Jacobians\n",
    "        x[5] = x[5]\n",
    "        dstate.append(0)\n",
    "    else: # otherwise\n",
    "        x[0] = x[0] + (x[3]/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2]))\n",
    "        x[1] = x[1] + (x[3]/x[4]) * (-np.cos(x[4]*dt+x[2])+ np.cos(x[2]))\n",
    "        x[2] = (x[2] + x[4]*dt + np.pi) % (2.0*np.pi) - np.pi\n",
    "        x[3] = x[3] + x[5]*dt\n",
    "        x[4] = x[4] # Constant Turn Rate\n",
    "        x[5] = x[5] # Constant Acceleration\n",
    "        dstate.append(1)\n",
    "    \n",
    "    # Calculate the Jacobian of the Dynamic Matrix A\n",
    "    # see \"Calculate the Jacobian of the Dynamic Matrix with respect to the state vector\"\n",
    "    a13 = float((x[3]/x[4]) * (np.cos(x[4]*dt+x[2]) - np.cos(x[2])))\n",
    "    a14 = float((1.0/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
    "    a15 = float((dt*x[3]/x[4])*np.cos(x[4]*dt+x[2]) - (x[3]/x[4]**2)*(np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
    "    a23 = float((x[3]/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
    "    a24 = float((1.0/x[4]) * (-np.cos(x[4]*dt+x[2]) + np.cos(x[2])))\n",
    "    a25 = float((dt*x[3]/x[4])*np.sin(x[4]*dt+x[2]) - (x[3]/x[4]**2)*(-np.cos(x[4]*dt+x[2]) + np.cos(x[2])))\n",
    "    JA = np.matrix([[1.0, 0.0, a13, a14, a15, 0.0],\n",
    "                    [0.0, 1.0, a23, a24, a25, 0.0],\n",
    "                    [0.0, 0.0, 1.0, 0.0, dt, 0.0],\n",
    "                    [0.0, 0.0, 0.0, 1.0, 0.0, dt],\n",
    "                    [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "                    [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "    \n",
    "    \n",
    "    # Project the error covariance ahead\n",
    "    P = JA*P*JA.T + Q\n",
    "    \n",
    "    # Measurement Update (Correction)\n",
    "    # ===============================\n",
    "    # Measurement Function\n",
    "    hx = np.matrix([[float(x[0])],\n",
    "                    [float(x[1])],\n",
    "                    [float(x[3])],\n",
    "                    [float(x[4])],\n",
    "                    [float(x[5])]])\n",
    "\n",
    "    if GPS[filterstep]: # with 10Hz, every 5th step\n",
    "        JH = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 1.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 1.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "    else: # every other step\n",
    "        JH = np.matrix([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 1.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])        \n",
    "    \n",
    "    S = JH*P*JH.T + R\n",
    "    K = (P*JH.T) * np.linalg.inv(S)\n",
    "\n",
    "    # Update the estimate via\n",
    "    Z = measurements[:,filterstep].reshape(JH.shape[0],1)\n",
    "    y = Z - (hx)                         # Innovation or Residual\n",
    "    x = x + (K*y)\n",
    "\n",
    "    # Update the error covariance\n",
    "    P = (I - (K*JH))*P\n",
    "\n",
    "\n",
    "    # Save states for Plotting\n",
    "    x0.append(float(x[0]))\n",
    "    x1.append(float(x[1]))\n",
    "    x2.append(float(x[2]))\n",
    "    x3.append(float(x[3]))\n",
    "    x4.append(float(x[4]))\n",
    "    x5.append(float(x[5]))\n",
    "    Zx.append(float(Z[0]))\n",
    "    Zy.append(float(Z[1]))    \n",
    "    Px.append(float(P[0,0]))\n",
    "    Py.append(float(P[1,1]))\n",
    "    Pdx.append(float(P[2,2]))\n",
    "    Pdy.append(float(P[3,3]))\n",
    "    Pddx.append(float(P[4,4]))\n",
    "    Pdv.append(float(P[5,5]))\n",
    "    Kx.append(float(K[0,0]))\n",
    "    Ky.append(float(K[1,0]))\n",
    "    Kdx.append(float(K[2,0]))\n",
    "    Kdy.append(float(K[3,0]))\n",
    "    Kddx.append(float(K[4,0]))\n",
    "    Kdv.append(float(K[5,0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uncertainties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11a6e5450>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7X3zxRc2fP18XXnihrrrqKhcqrCrZ7QIAAEDDZRgqDCDWPpwg7VrhdhW1076vdNGjET3k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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a621b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.semilogy(range(m),Px, label='$x$')\n",
    "plt.step(range(m),Py, label='$y$')\n",
    "plt.step(range(m),Pdx, label='$\\psi$')\n",
    "plt.step(range(m),Pdy, label='$v$')\n",
    "plt.step(range(m),Pddx, label='$\\dot \\psi$')\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.title('Uncertainty (Elements from Matrix $P$)')\n",
    "plt.legend(loc='best',prop={'size':22})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NqMs9oVGNFVBVtQ3DSZImzoCSJHVSHwPKc1CSpE4aOqCSnNzO2Nsw0PYTC7Rd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11aeced90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Covariance Matrix $P$ (after %i Filter Steps)' % (m))\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,4.5])\n",
    "plt.ylim([4.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kalman Gains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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V/erT943VfXixug8vDjtGre7+dKoe+/UJYccAAASsNA5XTgAgFjOXl8St7dHF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\n1qvL7jIVVe5Qu+rGn7EKtNZn/ypRz69tUduuVS0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L9cmgQ2PSHpJDzwceUNsTRuy9sl16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\nAADPNTl0+UCcc1skndrA+rWSzqq3/Jyk5xrY7+BG2n1S0pPRZMtI/oD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EAAAA\nLUlEQVQAAADSCoUuAAAAACCtUOgCAAAAANIKhS4AAAAAIK1Q6AIAAAAA0sr/B4DQA/zB5nmCAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a794690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.step(range(len(measurements[0])),Kx, label='$x$')\n",
    "plt.step(range(len(measurements[0])),Ky, label='$y$')\n",
    "plt.step(range(len(measurements[0])),Kdx, label='$\\psi$')\n",
    "plt.step(range(len(measurements[0])),Kdy, label='$v$')\n",
    "plt.step(range(len(measurements[0])),Kddx, label='$\\dot \\psi$')\n",
    "\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
    "plt.legend(prop={'size':18})\n",
    "plt.ylim([-0.1,0.1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State Vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FLHzoI/aU1/HAxVP59YVTCA2yLp9m8DluXBKLv38c954/mdKaRi59ZDnXPbWS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\nh/UhNC8W9zIQNYskvDVZXhqc2srG42mcxZ2pd3awdEQ3JY/ibnabjyeXW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3vzMhXCM0GjqNx8ukOL99BP379iempcy7E6LRMvtAx7HG/aUvctfwdky/fQA2h4Obp63n2o9+\nZ/rv6WzPKj7robTVdgdVeXs5pJvRoUVI3cfeVLTqBUCAvZRAHy+yiiooLq/FFfjiLOyWfArLrGTT\nnDYRgXUUqKjPGkDTtMar+LBx5q9VfDcPRyIarbA46DAGUpdA9mbjH0CfmyGmH9f2j6XQYuWNn1O4\n8O0VLH90JOkFFm6etp7MwxXHbcrHy8SITpHcM7wdg4MOwoYQaN7p6JAjIRqD9qOgqhTsVdD5Yk9H\nI4Rwtc4Xw57Fxv1lrzJ89DP8+tgopv22j1kbMnh+XjIAIX5m/nF5Dyb2jj7lpixVNvq/spSKaju+\nWHnBXEaneJn3XytmXwiJgYJUnhgzlud/SuWh2Zv5/LZzbNG2fS5r0wr5zj60piq/aPwk4fWU/FTS\n8y385ujB1b2kmIFwoa6XGP+0hqyNsPlL2DwdWnQHbz/uHdGelIMlfL8lm3ZPL8DHbKLa7uCJcV0Y\n0SkSm8M4q921VQjeXiawWeHnfzi33QDbUQhxOmZf6HWNp6MQQriLUnDhS7D0BbDkwg8P4d9uJPeP\nvJz7RrZnb56FbVlFPDI7iYdmbaFvXDNiwwNO2MwHy1N5a9EuzNhQmDBhfHb2GTHRzW+oEQqLg5JM\nbu7uzauLTPy6K495W7JOefJBa82SHYeYsS4Dq83BPSPaMbJzFFQUkZ+xg/35FjboLnw9oaub34jw\nFEl43ayyopzCzF20PvATGYUVJOs2vNOxuafDEk2BUhDTHw4mQc5WWPgEdL0U2o3i/67tzerUAvws\nB3jU5ydGdo+lmWU5pLYwhnsV7IWsfMjdATh7+fqHQ1isR9+SEEIIUWv+YUbSu+wVcFRD2q+Q9isq\nqhsdovvToZUvXN2VR+bs5Pl52/nsD1cXf0vN561FKdzh9TPtVTaju0YRFeyLScWBt49n3lNj0roP\nZKyBrE18f/9Yxr+7ihfmJ3NR95b4eXuRdKCIp77dxoHCcny9vbBU2aiothMW4I3N7uDDz6dTGrQe\nBZRUVLPY0Y85955vnMQXTUKDSHiVUuOAdwEv4L9aPuHZuQAAIABJREFU6zc8HNI5W/jtZ5TvXFrz\nuDIwRn7hhHv1uxWWPA/WMtj5AxxMwmvIIySO3YfO2Y5S0YADHA4ozoTEaUdfG+I8m9qyJ3Qa54no\nhRBCiLrnHwYTpkBlCaz4p/EZmbvDeaIXrgAc/lkkpbYmd9Fqoi58ELzMUHGYvbOe4DVzIRN6tSLU\nP+747bbs5f730thEdDBu01fRtcdVvDyxO8/PS+aGT9by2pU9mfjBbwT6eHFF32hsdo2ftxf9wiyM\nL/kf2lZFcnYxh8vNmE2K9NYTuLTnaPrHh3v2PQm3UlprT8dwWkopL2A3MAbIBDYA12utd5zqNf37\n99eJiYluivDspO7dw6dfz8SrspA95k68/Jeb6Nwy2NNhiabIUgDLXj5xeZ+bjCvBAPmpYKsEkxma\nd5S2Q0IIIZoOqwUs+XB4H+RsJy2vlLUb1gMwrFMksZHN2J2VR2L6YWLDAxh2/mA4705jCpHZ1xhZ\nJerGr29A6UHoNB46j+Op6UtI3bmVcFVKFd48cVFHug4Ya5y42DEf9v5y9LVBLaH/7UYXC9FoKKU2\naq37n9G6DSDhPR94UWt9kfPxUwBa69dP9Zr6nPAeYXdo7A6Nj1mu7goPspbD2g9BO4zEts9NEN7W\n01EJIYQQ9dL8LZms+d9UWqkCqrQ3fsrKDkc8rz/9NM2CfD0dXuNVXgi/vGTcV16g7RwqqSK3tJLo\nMH/CA08ydLzdSOh+hTujFG50NglvQxjSHA0cOOZxJjDQQ7HUGS+TwsskZ/6Eh/kEwPDHPB2FEEII\n0SBc1juGhNiXmbJ4Nz8kZQNwz4h2kuy6WkA4JFwPO+YZV8/t1bQYdj0tWiWAMhltFzPXG1Ovqkqh\n321Ge0YhaBhXeK8Gxmmt73Q+vgkYqLV+4A/r3Q3c7XzYGdjl1kDPTnMg39NBiEZHjivhKnJsCVeQ\n40q4ghxXwlXk2Kpf2mitI89kxYZwhTcLOLYUbIxz2XG01h8DH7srqNpQSiWe6SV4Ic6UHFfCVeTY\nEq4gx5VwBTmuhKvIsdVwNYQJpBuAjkqptkopH2ASMN/DMQkhhBBCCCGEqOfq/RVerbVNKfUAsAij\nLdE0rXWyh8MSQgghhBBCCFHP1fuEF0BrvQBY4Ok46lCDGHotGhw5roSryLElXEGOK+EKclwJV5Fj\nq4Gq90WrhBBCCCGEEEKIc9EQ5vAKIYQQQgghhBBnTRJeN1NKjVNK7VJKpSqlnvR0PKL+UkrFKqWW\nK6V2KKWSlVIPOZeHK6WWKKX2OG+bHfOap5zH1i6l1EXHLO+nlNrmfO49pZQ0gW7ilFJeSqnNSqkf\nnY/luBK1ppQKU0rNUUqlKKV2KqXOl2NL1JZS6hHn5+B2pdRMpZSfHFfiXCilpimlcpVS249ZVmfH\nklLKVyk127l8nVIq3p3vT5ycJLxupJTyAj4AxgPdgOuVUt08G5Wox2zAo1rrbsAg4H7n8fIk8IvW\nuiPwi/MxzucmAd2BccCHzmMO4N/AXUBH579x7nwjol56CNh5zGM5rkRdeBdYqLXuAiRgHGNybIlz\nppSKBh4E+mute2AUMJ2EHFfi3HzOiT/3ujyW7gAOa607AFOBf7rsnYgzJgmvew0AUrXWaVprKzAL\nmOjhmEQ9pbU+qLXe5LxfivHFMRrjmPnCudoXwOXO+xOBWVrrKq31PiAVGKCUagWEaK3XamPS/vRj\nXiOaIKVUDDAB+O8xi+W4ErWilAoFhgOfAmitrVrrIuTYErVnBvyVUmYgAMhGjitxDrTWK4HCPyyu\ny2Pp2G3NAS6QkQSeJwmve0UDB455nOlcJsRpOYfE9AHWAS201gedT+UALZz3T3V8RTvv/3G5aLre\nAR4HHMcsk+NK1FZbIA/4zDlc/r9KqUDk2BK1oLXOAqYAGcBBoFhrvRg5rkTdqctjqeY1WmsbUAxE\nuCZscaYk4RWinlNKBQFzgYe11iXHPuc8syil1sUZU0pdAuRqrTeeah05rsQ5MgN9gX9rrfsAFpxD\nA4+QY0ucLed8yokYJ1RaA4FKqRuPXUeOK1FX5FhqnCThda8sIPaYxzHOZUKclFLKGyPZnaG1/ta5\n+JBzOA3O21zn8lMdX1nO+39cLpqmIcBlSql0jGkVo5VSXyHHlai9TCBTa73O+XgORgIsx5aojQuB\nfVrrPK11NfAtMBg5rkTdqctjqeY1ziH4oUCByyIXZ0QSXvfaAHRUSrVVSvlgTISf7+GYRD3lnPPx\nKbBTa/32MU/NB25x3r8FmHfM8knOCoFtMYoorHcO0ylRSg1ybvPmY14jmhit9VNa6xitdTzG36Bl\nWusbkeNK1JLWOgc4oJTq7Fx0AbADObZE7WQAg5RSAc7j4QKMmhZyXIm6UpfH0rHbuhrjM1auGHuY\n2dMBNCVaa5tS6gFgEUaVwWla62QPhyXqryHATcA2pdQW57KngTeAb5RSdwD7gWsBtNbJSqlvML5g\n2oD7tdZ25+vuw6hM6A/87PwnxLHkuBJ14a/ADOdJ3TTgNoyT63JsiXOitV6nlJoDbMI4TjYDHwNB\nyHElzpJSaiYwEmiulMoEXqBuP/8+Bb5USqViFMea5Ia3Jf6EkpMOQgghhBBCCCEaIxnSLIQQQggh\nhBCiUZKEVwghhBBCCCFEoyQJrxBCCCGEEEKIRkkSXiGEEEIIIYQQjZIkvEIIIYQQQgghGiVJeIUQ\nQgghhBBCNEqS8AohhBBCCCGEaJQk4RVCCCGEEEII0ShJwiuEEEIIIYQQolGShFcIIYQQQgghRKPk\n0YRXKTVOKbVLKZWqlHryFOuMVEptUUolK6VWuDtGIYQQQgghhBANk9Jae2bHSnkBu4ExQCawAbhe\na73jmHXCgDXAOK11hlIqSmud65GAhRBCCCGEEEI0KJ68wjsASNVap2mtrcAsYOIf1rkB+FZrnQEg\nya4QQgghhBBCiDPlyYQ3GjhwzONM57JjdQKaKaV+VUptVErd7LbohBBCCCGEEEI0aGZPB/AnzEA/\n4ALAH/hdKbVWa737jysqpe4G7gYIDAzs16VLF7cGKoQQQgghhGg4dFEGhy3VAIS1bIPJq76nRuKI\njRs35mutI89kXU/+VLOA2GMexziXHSsTKNBaWwCLUmolkIAx9/c4WuuPgY8B+vfvrxMTE10StBBC\nCCGEEKKBy9tF4uxX2Z1TCkB4kA/jnpzt4aDEmVJK7T/TdT05pHkD0FEp1VYp5QNMAub/YZ15wFCl\nlFkpFQAMBHa6OU4hhBBCCCFEI6J//7Am2fX19qKwzErl3t88HJVwBY8lvFprG/AAsAgjif1Ga52s\nlLpXKXWvc52dwEJgK7Ae+K/WerunYhZCCCGEEEI0fHkVDgD2xkykS8tgAL79bArFBYc8GZZwAY8O\nVNdaLwAW/GHZf/7w+C3gLXfGJYQQQgghhGiktKag2ALAhWMupV1GPkkHjKu7yxK3c8VFLTwZnahj\nTWZmdnV1NZmZmVRWVno6FCEA8PPzIyYmBm9vb0+HIoQQoqnTGpTydBRCuEfFYYorrAD0ignFP2AM\no7P2sCwll+zDFg8HJ+pak0l4MzMzCQ4OJj4+HiV/0IWHaa0pKCggMzOTtm3bejocIYQQTdnCp6C6\nHCZMhfJ8CIgAk5enoxLCdRw2qmzGkOZAXzO0SqDF+Ccg5VFK8v9YQ1c0dJ4sWuVWlZWVRERESLIr\n6gWlFBERETLiQAghhMdpaznbs4rZ9emdsPxV458QjdnBJA4WVbI1YFDNIhUUhZdJYVIODwYmXKHJ\nXOEFJNkV9Yocj0IIIeqDnTklbM0sBsDspSi3FtPzAg8HJYQrpfyIQ2sq/KOOLjP7ERHkw+FcaW3a\n2DSphFcIIYQQQhwvq+zo/XVphQDY0w7Su10rD0UkhGsdGc7cK+qYOipeZkBRaPP1TFDCZZrMkOb6\nZvDgwZ4OQQghhBCC6soTi/SkpKZ6IBIh3MPqTHjjIwKOW24LiKKMgJrnReMgCa+HrFmzxtMhCCGE\nEKKpO7Ce4gobEUHHX9U6mJfvoYCEcL2iimoArIExxy2P9S6hh9pHdlGFJ8ISLiIJrxBCCCFEU2Sv\nRm+egdaalJAhtIsMrHkqq6DUg4EJ4Vpp1eFU4U37Tl2PWx7sZ8z23F9Y7omwhItIwutmffr0IScn\nh2effZbPP/+cFStWMGnSJE+HJYQQQoimxmGjtNK40mVu1YNB7SK4YWAcvt5eRFamezY2IVwoyJrH\nPt2SjlFBxy23teoPQGGZXOFtTCThdSObzUZhYSEtW7YkKSmJ3r17k5SUREJCgqdDE0IIIURT47CT\nVWS0x+vYJgbGvgpj/kGwn5l2liQPByeE6+RXKIK97Cd0zIhoFgbAwYMHPRGWcBFJeN0oJSWFLl26\nALBjxw66detGUlISvXr18nBkQgghhGhyHDbS8o0Szed3jgbfIPALIcDHi2q7g+rkHz0coBAu4HDg\nTznptvATngoObwlASaEkvI1Jk2xL9NIPyezILqnTbXZrHcILl3Y/7Tq7du2ic+fOFBYWEhQUhI+P\nD4mJibz++ut1GosQNUoOovcsxmatwnvgnWCSc1xCCCGcqkooLq9mb/gwggMDTng6ZdUcena/xAOB\nCeFC9iocDoht5nfCUyb/UAD87CdWLhcNV5NMeD3Fx8eHlJQUEhMTSUhI4KuvviI+Pp6oqKg/f7EQ\nZ0NryN9N8rdvsCe3jPIqG1EV7bhw9IWejkwIIUQ9oR12ALwj2hy3fEDbcDIKytmWWUxPTwQmhCvZ\nrRRarJSGnHiFl7A4gvzM7MjJdH9cwmWaZML7Z1diXWXcuHEsWbKEyZMn4+/vT3h4ONOnT/dILKKR\nO7gFnfg5SQeKahbt2rFFEl4hhBA1qgoPABATEXLcch+vo6OBSiqrCfHzdmtcQrhUZTE+ZhMOu+3E\n5/xC8TIpSq3uD0u4TpNMeD3F29ub9957j9LSUm644QbGjBnj6ZBEY5WZSFq+MRzHLzIea8F+8i3V\nxpXfPxRoEEII0TRVb54NgEP94etgWBx925Syaf9hdmYeZmAHGYkmGhGtKamopllM6xOfUyZ8vEy0\nqspyf1zCZWRCnwds3bpVClUJl8rNzmBdWgEAbS55Ah9fP3pWboTf3vVwZEIIIeqLEocxh7FZdMfj\nnxh4LxGBPgAcOJDu5qiEcDFtDOWvcpzkAoBSRAT5YLEp7A7t5sCEq3g04VVKjVNK7VJKpSqlnjzN\neucppWxKqavdGZ+rbNy4kRYtWng6DNGI5eVm19zv264Fkf6Kymo7c5auQmsN5YVQmuPBCIUQQnha\nfrmdCnxpGfaHglU+gQS2HwRAen6pByITwnWqy43pXvHNg0/6fKFPDNEqn+KKaneGJVzIYwmvUsoL\n+AAYD3QDrldKdTvFev8EFrs3QiEargqr8Uf6mguHoJTC38cLAKvNwZqZr2Fb/CLli1/xZIhCCCE8\nyWqhoiQff6ro3jrkhKcDonsAEJu/yt2RCeFSRTn7AajUJ5/ZGRWgqcZMaaUkvI2FJ6/wDgBStdZp\nWmsrMAuYeJL1/grMBXLdGZwQDZa1nMPlVvYQi/ewhwHoGR1K6zB/APbvSOSbxAN8v1nmpwghRJNV\nUUSVzQFAgM9Jvvj7NwMFulKu8IrGxSdtCQDRLU8+2rLCryURlJBfVuXOsIQLeTLhjQYOHPM407ms\nhlIqGrgC+Lcb4xKiYbOWYamyk+3dBryMLzG+0b0Y2TmS8T1bHbdqiZy9FEKIpknbsdoczDWNPfnz\nzdoS5u9Ntk+bkz8vRANVVmVUZ7aZT+w9DRAebCwvKZfvSI1Ffa/S/A7whNbaof6ksqxS6m7gboC4\nuDg3hCZEPVVRRGW1He+QZkeXnXcn2KtpVlmE946/UG03zuoXl0u7CSGEaJIqizlcXk1cZNjJnzeZ\nMJtMHMwrcG9cQrjYYa9ISiinV4tmJ33eFBgBwKFiizvDEi7kySu8WUDsMY9jnMuO1R+YpZRKB64G\nPlRKXX6yjWmtP9Za99da94+MjHRFvEI0CNpuxeHQNAs9Zk6WUmD2gaAoLugaRYi/keTmlVZ6KEoh\nhBAe5bBjsztwmE5/0rO9d6GbAhLCPaoryzigIwkLOPmxHxZkVC/3sst3pMbCkwnvBqCjUqqtUsoH\nmATMP3YFrXVbrXW81joemAPcp7X+3v2hCtFwlFuM+VbtY1ud9Pnw7heQEGuc0bdUSmd1IYRoimw2\nY7hmYMjJr3IBBAf4UFwunxOicakoKcCEgxYhfid93tfHF4C0g/nuDEu4kMcSXq21DXgAWATsBL7R\nWicrpe5VSt3rqbiEaOjKctMBcJgDT75Cz6txtB0NgP7pUaoPbHZTZG6Q/B2s+j9PRyGEEPWeteQQ\nAJ1bn2JIM5Dr1QofqrE7p8EI0eBpjc3hoJggvL1OngYFhTUHIMwsJ3saC4/24dVaL9Bad9Jat9da\nv+pc9h+t9X9Osu6tWus57o9SiIalOC8TgMjIqFOuExDRGoDMwnKWfPmGW+Jyh6rdyziUsQe0NIsX\nQojTKa6wA1DOyQv3AIQF+tJCHab827+6KywhXKuqlKpqB15epyljpLwwmRSOyjL3xSVcyqMJrxCi\n7qm8FADiwk/9JSbY36fmfmW13eUxuYW1nHlbsvhl5yFyS8o9HY0QQtRrjiKjUUabqFNf4Y3nIAA/\nJGW7JSYhXM5hQynwaRZ96nX8jWH+GblFbgpKuJokvB4yePBgT4cgGimrs6/iqeamAPj5+OBtNn79\n91lD0Y3hiuj2OdjsxvvYmSVFVoQQ4nSsGAV7/H28TrnOkf7tQjQaDjv5ZVZ8fU5TrM3sh7eXidY+\ncoW3sZCE10PWrFlzyucqKioYMWIEdrtx5e29996ja9euTJ482eVxBQUF1dxXSnHjjTfWPLbZbERG\nRnLJJZeQnp5Ojx49jnvtiy++yJQpU1we46m48//pTFmtVoYPH47NZnPPDrWmqLyaSnyIDPY99Xom\nM1f2iaZjiyBaqUI27trvnvhcqLKyouZ+YYEUmhBCiNMpslSSTwina/ro7aVoF3mKehBCNESVxfia\nTSjHaeal+wQS6ONFrqURXAwQgCS89dK0adO48sor8fIyzrp++OGHLFmyhBkzZhy3ntYax+l+YWsp\nMDCQ7du3U1FhJBJLliwhOvo0Q0Bc6Eze66n+n851e3XBx8eHCy64gNmzZ7t8XwBUlVJWZWOz6oKX\n6TRfY/zD8DIpOkQGA7Bl3TL3xOdCWYdya+6X5P+xw5kQQohjmbQNByZimp3+Kq5SxmeJpcpNJ26F\ncCHtsFFhtRMedfJOFgCYvLDaHVRapWhVYyEJr5v16dOHnJwcnn32WT7//HNWrFjBpEmTjltnxowZ\nTJw4EYB7772XtLQ0xo8fz9SpU0lPT6dz587cfPPN9OjRgwMHDvD222/To0cPevTowTvvvANAeno6\nXbp04dZbb6VTp05MnjyZpUuXMmTIEDp27Mj69evPKN6LL76Yn376CYCZM2dy/fXXn9P7vvzyy+nX\nrx/du3fn448/BsBisTBhwgQSEhLo0aPHCUnhyd4rwFdffcWAAQPo3bs399xzD3a7/YT/p5Otc7Lt\nnWy9I/vu2rUrd911F927d2fs2LE1if/06dPp1asXCQkJ3HTTTaeM6dj3fiZJeJ2wWzEpo6n6aSnj\nZMqRHnT2nB2ujszlysuPztu1SUVRIYQ4LWvhARQaX/OphzTT4yrCnH3bj0yXEaIhs5YVAFBhP81x\nr7wI8fPGW7KkRkN+lG5ks9koLCykZcuWJCUl0bt3b5KSkkhISKhZx2q1kpaWRnx8PAD/+c9/aN26\nNcuXL+eRRx4BYM+ePdx3330kJyeTn5/PZ599xrp161i7di2ffPIJmzcbbWZSU1N59NFHSUlJISUl\nha+//prVq1czZcoUXnvttTOKedKkScyaNYvKykq2bt3KwIEDz+m9T5s2jY0bN5KYmMh7771HQUEB\nCxcupHXr1iQlJbF9+3bGjRt3wuuOfa9t2rRh586dzJ49m99++40tW7bg5eXFjBkzjvt/Gjdu3EnX\n+eP2ysvLT7nekXXvv/9+kpOTCQsLY+7cuSQnJ/PKK6+wbNkykpKSePfdd08Z0xE9evRgw4YN5/T/\ndtYqiiiwWIlv/idD0ALCAVC9rsXfx4syi8UNwblWUVkFhRhXrN02hFwIIRoomzkAjaJZoM+pV2oz\nlCrvEADyy6rcFJkQrmMvNwpRRbc8dScLlMLbbCKo6pCbohKudpqa3I3Y9m+hpI6HPIZE8//snXd4\nHMXdgN+5piuqp15tufdeaKbYQAymxxAgDQgJ+b7wQQKk0dJIIKSShJAQkpAGCYFQbMAUF2yDu3Hv\nsmX1Xq73+f6Y00mnLllyy77Po0d3u7O7v727nZlfHabc0GuTAwcOMGHCBAD27dvHpEmT+PWvf80N\nN7Qf19DQQGpqzxUTAUaMGME555wDwPr167n++uux2ZSCc8MNN7Bu3TquueYaiouLmTp1KgCTJ09m\n0aJFCCGYOnUqpaWl/bqtadOmUVpayosvvsiVV14Z294W4tSZnrb/6le/4tVXXwWgvLycw4cPM3Xq\nVO6//36++c1vctVVV7FgwYJe7xVg5cqVbNu2jblz5wIq3zkrK77T6qnNhRdeGHe+vs5VXFzMjBkz\nAJg9ezalpaU0Nzdz4403kpGh1miz2+288MILvZ5Hr9djMplwOp0kJSV1+/kMGZEQBp1AJPRxHaMF\nrn4KgIzE39Lc1EQ4InsPgz7NibjqCEozer2gvlarKKqhoaHRG5FwmEaZjK2XolXodPgypyGPlOE9\nWyr6a/xX4/CqMGWXSOy5kRCEI5J6n+YXPFv471R4TxEHDx5k/PjxNDU1kZiYiMlkYuvWrTz++OOx\nNhaLBZ/P1+t52pTbvkhIaC9apNPpYu91Ot2APGDXXHMNDzzwAGvWrKGxUYWCpKen09zcHNeuqamJ\n4uLiLsevWbOG999/nw0bNmC1Wrn44ovx+XyMGzeO7du389Zbb/Hwww+zaNEiHn300V7vVUrJ5z//\n+bjPrDM9tSktLY07X1/n6vj56fX6WEhzf6/XEb/fj9ncc9XkoSLsqicQipCYnNLvY3S2dBxNTlq9\nQey9WfpPc/RC0EQSRXoH1gSta9PQ0NDoDWdrIxGSejRUt2GzqLErqKWKaJwF+ANBAArTe59LS4ud\nfKEVwDxb+O+cFfbhiR0uTCYTBw4cYOvWrUyfPp2///3vjBw5Ms4bmJaWRjgcxufz9UtBWrBgAbfd\ndhvf+ta3kFLy6quv8re//W1I5b7jjjtITU1l6tSprFmzBlDVnHNzc1m1ahULFy6kqamJFStWcO+9\n93Y5vrW1lbS0NKxWKwcOHGDjxo0AVFVVYbfb+cxnPkNqairPPfdcn7IsWrSIa6+9lq997WtkZWXR\n1NSE0+lkxIgRfbYZzLk6s3DhQq6//nruu+8+0tPTaWpq6vM8jY2NZGRkYDT2UgJ/iAiElAU+wTIA\nT3LqCLLK11Pe5DlzFd6glwZ3AGtqNonhWo43aEsJaGhoaPRGkghgph9hykKPQFJa72b2CPvwC6ah\nMYy460sBSOzDMJ6kVyteRCIS3Rkc/aah+O9UeE8Rixcv5r333uPTn/40FosFu93OX//61y7tLr/8\nctavX8+ll17a5zlnzZrFbbfdxrx58wC48847mTlzZr9DlvtDQUEB99xzT5ftf/3rX/nKV77Cfffd\nB8B3vvMdRo8e3aXd4sWL+d3vfsfEiRMZP358LKR49+7dfP3rX0en02E0GnnmmWf6lGXSpEk89thj\nXH755UQiEYxGI08//XScktpTm5ycnAGfqzOTJ0/moYce4qKLLkKv1zNz5kyef/75Xs+zevVqlixZ\n0ue9DQWeqBc60957WHxHslKsHAd2VrQwvbD/x51WeJow6QUNYRvBcIREozY4aWhoaPRGCB26pF7y\nGKOk2pTx3SS02ggaZz4BYSGInjRr7wZ+lzkHPTU4/SFSLMPvsNAYXoSUZ98aU3PmzJFbt26N27Z/\n/34mTpx4iiSK5/bbb+fWW2/lsssu63b/9u3b+cUvfjHknlqNU8MNN9zAE088wbhx47rsG+rfZcWq\nP7B21VuEFv+Ez10wpl/HuHYt542X/sjmCd/gl585d8hkOanUH+KFp75J5aibON/xJitbc3nkOz85\n1VJpaGhonLYse+wmtptm8p1vfLvXdvVbX+O91/6C7crvc+15U0+SdBoaw8Oqvz/J7gP7uf5rT1OU\nbu2x3fp/PMb2/Ye5/r5nKLT33E7j1CGE2CalnNOftlo29ilg165dTJs2rcf9s2bN4pJLLolb2kbj\nzCQQCHDdddd1q+wOB56IskIWZSb3+5jEBFWwxFS9bVhkOilEQgghaJI2QpEILX6ta9PQ0NDokaAX\no0GHDHRfm6IjukRVpLGqSUsV0TjzSfMdJyIF9sTePbxppghJePFry3GdFWizwlPAtm3byM7O7rXN\nHXfcgV7fS+VEjTMCk8nE5z73uZN2PYfHhwsLRv0AHu3EbJLMRs7xrBk2uYabgKMOKSWjMpPRW9Mp\n1Kn3GhoaGhrdEPITDEewZIzss2miRRVw1AutT9U48wkHPBhFqPfq5EDAmEIQA5UtfRuFNE5/NIVX\nQ+MswuyrJYIgP9XS/4PyZmI16QmcwVZMZ3MdABFzCglGPW5p1qyyGhoaGj0RcOP0BgnJvusdJOgF\nQggMAcdJEExDY3hx+CIcl9l9VidPSUlBR4SIZjw/K9AUXg2Ns4gat8RMAJNhAI+2EBjSCiiPpA+f\nYMNMk1NZYDPs6bgNdvREqHP0o/qohoaGxn8j7np0QmC19GO5PHMqAijTQpo1znSkxEiIsKnvtC+j\nwYAVP3WO3pcK1Tgz0BReDY2ziLRgLRUyk5zkga3569InoydCkzswTJINM95GPCSQnWIlPdlCgain\n2XOG3ouGhobGMBM8spqIlCTb+hENpDcSkRLWlpmfAAAgAElEQVSTNmPUONMJuGn2BEhO6PvHbI1W\nJXd7NeP52cAp7b6EEIuFEAeFEEeEEN/qZv+nhRC7hBC7hRAfCSGmn8j1tJw+jdOJ4fg9NvoEZhEc\n8Jpx2SmJ5IgmvMEzs1BaQ6sbMwFSrUYMUq2d16QpvBoaGhrd4kMZRb1p4/turNOTajVxpFYLadY4\nw4mECIUlXlPf60lb0vPVi7Cm8J4NnDKFVwihB54GrgAmAbcIISZ1anYMuEhKORX4AfDsYK9nNptp\nbGzUlF6N0wIpJY2NjZjNA/PE9nFSrGEHFZGMAR+qD3sJoqem9cwszhD2OaiUmRSkWbBmFGHFT0jL\n4dXQ0NDolhZvEAB7kq0frQWhSIQb5TsQ8AyvYBoaw4mvlWA4gtHQe4VmUEVHAY5W1Ay3VBonAcMp\nvPY84IiU8iiAEOKfwLXAvrYGUsqPOrTfCBQM9mIFBQVUVFRQX18/2FNoaAwpZrOZgoJB/6S74nfi\n8AYoTBl4dW9TehGwHW/gzFQSjd4GBAYSEwx4hLqHkppGLpucc4ol09DQ0Dj9cPqCVMl05qX1I6TZ\nZCPNaqK8yQP1+yF/9vALqKExHPhaCEckRTl9OwYMCcoYlGw6M+dFGvGcSoU3Hyjv8L4CmN9L+y8A\nbw/2YkajkeLi4sEerqFx+hNwI4TgeKjvUJ3O2MwmjIQ5WOPggrED9xCfUqTE5fURMuZi0OtIzlBG\nBItOG6Q0NDQ0uiPkbiKMHrutb08XMqKUXWB7uYNZ+cMsnIbGMOFpVGpHo0jtu3FCEhaTnpLKumGW\nSuNkcEaUIBBCXIJSeL/ZS5svCSG2CiG2al5cjf9KPA00uwNkZg/ca5wRjayuOROfnUgInRBUhNQA\n1lahuq7q+KmUSkNDQ+O0xeVyYhYBclL6kVZjtFKcobxdR+u0Ss0aZy7uoKpvMrqwH/MkvREBWOWZ\nmeqlEc+pVHgrgcIO7wui2+IQQkwDngOulVI29nQyKeWzUso5Uso5mZmZQy6shsZpj7cZAI8uccCH\n2uwq9Lek3j2kIp0UAi4aXX4KstIAMKYp94NZ8/BqaGhodItEUC9TSLUY+25sNDNnpIocam2sGmbJ\nNDSGD2d9BQBS148AV3MqZpOBsOsMdARodOFUKrxbgLFCiGIhhAm4GXijYwMhRBHwH+CzUspDp0BG\nDY0zBp9XhZylpg/c4CPCQYwGHbbmfX03Pt0IuAlFJA6pPBXCYMZs0uMPalWaNTQ0NLpDeBpBn4BB\n379poFGvPGPSMISFFjU0TjLO5loARmUl9d04IZnEBD0Rv1ao7Wygz55OCJEphPi9EGJ59P0kIcRt\nJ3phKWUIuBt4B9gPvCSl3CuE+LIQ4svRZo8C6cBvhRA7hBBbT/S6GhpnKx6n8vCmpw08h5fELCxG\nPZeFPhhiqYafiKueSESSlJSiNuj0IKGxrvrUCqahoaFxmuIPRfCFB7ZqhdGg43jjGRgFpKERRRd0\n48dIdlI/DDd6AyCwCwehsBYxdqbTH9Pe88AHtIcfHwbuH4qLSynfklKOk1KOllL+MLrtd1LK30Vf\n3ymlTJNSzoj+zRmK62ponI20trYAYDP3I0StM4k5ZCSacPlCQyzV8ON1qkyHvLxoF2VKxKAX2BIG\n8TloaGhonO1EIugEJCQPLBrIqNeRYjjzxggNjTYanF4OyQJSbf2bHySmpJMtmvEGw8MsmcZw0x+F\nN0tK+QIQAZBSBttea2honD74w+DAyoh068APTsykQZdOKzYikTNrreompyooIROiIUqGBBITDNQ3\nN59CqTQ0NDROU0JeWr1BzKYBGAXn3YXVqKehQatYq3Hmovc2EsRAcj8dA36dGZ80Ud3qG2bJNIab\n/ii8biGEHZAAQoi5gGNYpdLQ0BgwTU4vgehatIMhJ9GIiRBO75mV++qoOABAfma62qAz4g9FyBTO\nUyiVhoaGxmlK0IsQghbfAHwX2ZMQOh0hBr7Ou4bGaYGUSCnRD8Bnl5KZT65oot7pH0bBNE4G/VF4\nvw4sA0YJIT4AXgTuGVapNDQ0BkyirxqJjtwUy6CO91hzseBnyxvPDLFkw4u3WVUNHZ0VrU6t05GW\naMYT0SZmGhoaGl2IhJFSkpudO6DD9AlW9EE3Up5ZUUAaGgCE/DS6AtjS+790o0ko5bjZc2Y5AjS6\n0h+F92PgEuAi4F5gErB7OIXS0NAYOBUeHQkEsSUMTtEbl6hCdur2nlmFq3zOZupIpdDeHsrt09mw\nBhrPuPBsDQ0NjWFHhnH5Quj0Axsr0hIgGTeOM7DWg4YGfidGvY6QFP0+JMmeDUB5TY+romqcIfRH\n4d0spQxIKXdKKXdIKQPA5uEWTENDY2CY9ZJqacdqGmRIs8FDitWIQd//weB0wOX14ZA2Egztk7dE\n4Uci8Ie0cgMaGhoacXhVgcNgeGCKq7TYSRIeDtVq6SIaZyDeJpy+IKnp2f0+JDlDeYMNUgtpPtPp\nUeEVQmQJIaYDFiHEVCHEtOjfBcAgquJoaGgMJ5HmMsyDVHYBSM7DZjIQGuBSFacUVz1OX5CAOb7a\nqEwpRCBxBzRPhIaGhkZHwtGQ5OysgYU0pyeasOHnWL22NJHGmUckpMKSA4bEfh+TkKCWLzpWUTUs\nMmmcPHqbHS8B7gAKgN922O4EHhlOoTQ0NAaOQafDHzoBZdWagd1moqrFSzgi0etOf09v5NA7BEMR\ndNmj4raHhZ5c0UStw0dGYsIpkk5DQ0Pj9MPhUekrAy1AlZ5oxoKfRodrOMTS0BhWHHXHAUhJTur/\nQSbl3/P7hqlKc8AN3mZI6X9escbg6FHhlVL+GfizEOImKeVLJ1EmDQ2NgRL00uQOkJqWPvhzTL4O\n+dHbeEigqsUblxN7ulLbUA+AtXB63PZMsySIgUaXVmiiT1x1YEkDvbZusYbGfwNeh8pHTE00D+g4\na85YYBsNpXuAiUMvmIbGMOJqqgEgJ6+w/wclJGE26RHOYfDwLrsXTyBMndNHwad/i8FoGvpraMTo\nM4dXSvmSEOITQoj7hBAPtv2dDOE0NDT6ibcFXyhMNRmDP4chgXDheQA0us8MRbGyuhqAc8fFh+ZF\nkgtIxk2rN3gqxBo4rZWw7XmInOSc46APVv8Q9r1+cq+roaFxynA4VQ5uSlLygI7TFS9AJwQ4KodD\nLA2NYaXVryLgLAkDWMnCmk6K2YjPOcRFq1Y9xvJd1bz2cSUfHWnk+TfeGdrza3ShT4VXCPFb4PPA\nfYAF+AwwZpjl0tDQGAARRzVISElOOaHz6AwGrPhpdp8ZBRqanF4aSWbOiLS47XazCscua2g9FWIN\nGOe7P2LrR6twV+0/uReORHOcK7crZTsSgQEWsonD2wKeJnBUq3P2xK6XYPfLg7+OhsZw0FoJrvpT\nLcWwk1SqJtd6y8AUXqzpGPQCodOWfNM489CVbQCgKN3W/4OMVmwJeuy0EgwPnUG6uqocRweDfG3Z\n4SE7t0b39KdK8wVSyluBRinlI8B8NIVXQ+O0wrH5HwDYc0ec0HkyLGoic6y66YRlOhmEHLVUy3Rs\nCfHZGbZMlQ8jw+FTIdbA2PIcm441cqjWyZ9eX3FqZAi64c2vqb+37of6Q4M7z4e/hHU/gw+egO1/\n6b7NkZVw/EMoXTd4eTU0hoO1T8Lqx061FMNOi0dNtPPtA8hlBNCbyEhMwNtQNgxSaWgML55oEcsC\n+wA8vEJgMeqZIMqpcw6RIyDk50CNirK4/LaHsZr0eFrPfkPbqaY/Cq83+t8nhMgBfEDe8ImkoaEx\nUOqb1TITo0eO6qNl72TkKYW55KP/nLBMw079IVq9IZItXfNezCZVqOpwec3JlmpgBNwEKndS51AD\naXLDzpN37f3LYdPvut+38WlwDyCES0rlGfY2Q6CPgjb73+j/eXvD3QjHNKVZYwiQEgKeUy1FV/zD\ns/yPwxvkiMxnRPoA6zQIQTgi8Yb7M3XU0Di9cGGhQmaQlDCw1SxMSao2SkXTEPURzhoaXH5CxkQy\nxswGSxoZobqhObdGj/Sn13pbCJEK/BTYAZQC/x5OoTQ0NAZGtddAqcxmVqfQ3oFi1qkcl8nerQRO\n8zVsgx/+BiklY1K72ak3IYRA5yw/6XINCHc9L2+tiL01Bp1EIkOwLFS4h9zltnBjgCPvQWv75+ML\nRnD4OoQzV27t+fwH34aaPdEDW+GdB6FyW9d2zlrY8UJs3c8uOAZZCMTTBKu+D3teVnnIpxM9ffYa\npyeOalj+VXjn22w61sSqg6eJp6V0Pbz7MJSsHtrzRsK0+oI4sWA2Djw0WdjSyRON+IJnQPTM2cKJ\nppoMF+GgSgHwOVSffDojJW5HCw5zHkIMbAUKU9EcAA7VOoZGFF8LwVCEY1mLAEi1GvFKo/ZMDTP9\nKVr1XSlli5Ty30AxMFVK+e3hF01DQwMpVa6jqxfrXySCx9VCtUwn/USX4NEbmZKv8oCP1Q5xkYYh\n5lCd8iR6p36m6860kZiNOlye0zwXuYMXtTjDRgg9H5Y0nNg5yzbCWw90r2Su/J4KN47ED6yVzV7+\ns72C5TurqGzx4vaHIeiNP1ZKaDgMIT8cWgFb/qC2O2sh6IFjH3S93pofQfkmOLZWvd+mwpyPNbjZ\nUNIIB94c+P2F/LDye4TbDAPyNJkkeJuheqf67Fu1oj5nCuHVj7PqQB1bSpspqXNR0+Kl/oUvq+9y\nKJFS/Xma1P8+CO14ibd217D7vR5SAwZLyI/HH8ZvyR7U4RlWpSzUDyS809ty8gvynU2s+6lKNTnd\n2PA0rH6M2le+wZY/3kt13WliLOqOcBB3IIRtEIsRZCSqKLLquhMcm6M41v0egKJMNdcypeZTJOoG\n9kxpDJgBxaVIKb3AdCHE28Mkz38vFVuVJ2Tnv/o1GGqcxniblddrKGguVbmOW//Uc5twALc/TIp1\nCNabTSkkPdq5l9ee3hbbytYgFTKTped2szyG0UqKxYjNdfzkCzYAWmuOACAnX8eYUaMwEGbz1s0n\ndtKyjeq/p1G97s7y7m+3VEckfHCofaLywcF6Xt9RSeved2HZvdASzder2Q0bfgNvf6P767p7mexE\nol7Pqu1UNHvZUNLIsQY34dpBFOna9zrBsORfW8pZf6RBGYMc1XB0zcDPNRS4G6GxBN7/bvtz2lRy\namQZLH4nVO9SXqTTzWM+nPidHG1wU9Pq43Bte/jwe/tqeeHp7w5NlEskDBt+q7zIu1+Gld/D/cr/\n4Xr5K9DScwTKkQYPLZ4AuytaKa8bwr7Y10JYSuy2wS2BErHmkCVaqGzx9t0YlJHs/e+o+gCa0tsz\nkYj6PXQ3/2uril22Sa3b2pe3N+CON9g0H48/JuRXlflP0Gtce/wAb+6uZuX+Wg7XuvjD8388ofMN\nJ7JiM8FQBGEd+EoWydGaIM311UMiS3k0NDpv7CwALEaBDxN1zv+ivvcU0GMguxDiIuAZVL7ua8CT\nwJ9QlZp/eFKkO5s58KaaoF35EwgFaF7/JzaVNuILhJlhnsDI8dP7PMVpSTgEO1+AURdDatEQnzsI\nh99Tk+cJV4PuNM0jWvtTlcc46ToYfUn8voAbELHFzPuk5TgbShrJyZAU99Qm4MYfDKNPzToBoaOk\njSA84kI4+Ao+f0BZ5s0p0FMI0I4XwWSDSdec+LUHQiSCy+ulRZeDxdRNWJ45GVuCgRzRhMsfInGA\nOTsni5pWNcAljF1IZsYY2Lwbb8UeYEl8w0gY+lsZVUSfC28z7HwRzKkw+XrY9uf2Nu9/l92Vreyt\ndJBi7d7k/eauam6dX6SKUF36vbjc2zqnH4tRT9LKH7Q/5+EAUkJESvQ6weE6F1uONXHF1Fw6Btqv\n7aBcv7e3ksVXR980loA1HSydYtRLP4TMCWCLrjHtaaIqOtkua/QQWf9LdG0/zxEXgN6gJngH3oS5\nXwBDgvr8hK7n3/FAWPdzyJoEhfOgZFX3xbeOrITiC0/8WieLXS9Bza7293PvhJyp6nVLmTKa5M04\nNbKdCL5W1X/1QHjFQ2w5Fq9Mmk16fAEVNbD6ow184sLzB3bND56EgjkweiE0luBa/XPe2BEN3d/0\nQlzTERXfZsaN38aWPzn+HH4n9Y52hXLlhi3cdu0nur9e9U5VEX32bf36fYc8rQRDEVKyBjc+p9jT\nMRCmrNHFOaP6XvfdX3OAVzYpo9kNFzVjPrxc7Zj9+UFd/6wkElaRMLv+Bef8L2SOj9vt9odp9gRI\nWP9nki1GDDqBfs5tkDez++98z39USspF34K1TxKOFm+MSDAufgz2v4G7ZCMWnxPdrG4ipHpDSgi4\nCK/9GSv318btGuPYxJF/PciYpd877dZ1b96oCntmZWYO+FhhSQMBacEhqAkSDnKsQSm8CybmA2DL\nKMTKFkrqXMweYT/xa2h0S2+zwF8C9wAbgCuATcDDUsqnhuriQojFwFOAHnhOSvlEp/0iuv9KwAPc\nJqXsZa2LMwf//hU0uwPkfPgrmPJJ3t7Tbjna98qPGPngv/o+iateTWhnfRYsPeRuhvxqwteZ0vUQ\n8sGohT0rjiE/1B+EFGXdwtr3gyiPf8ja1Suo/M+rTDn3E0xb8uVODWR8Bx1wK4WpjXBQDd75s7p0\nmOHl97PucANVLV5GZ77M/Hv/1qc8Q8b2v6nPeOJVfbdtK9qz7zUwJUJyHhxYDnO/qHIdkwvgoq93\n/Sw6c+R9XDte5ViDm3X1Fr7hqoPETkqtt4Xg+98HIDM1cZA3F09SzmgAMnY/Cw06yJmmFIc2Dr8P\nSBh7GZRHvYknWeEN73gRXyBMZkbPE65EWyK5op7DtU5mFp1YbvNwUd/iwoWF2ZmJMOJ8Eky/pLq1\nk5XXUQ1rf6KUkOxJfZ5ThgM0OP2kb/+rWjPT16JyXVETp9d3xIfbNkfXXDbodYQ6LbsQikgMOqE8\nNB14f5+a6Nw63wCeBtz+MCaDjrf2VOP2hbh2Zn5Mkahq8ZJ2bC1Muh5vpxylJld0vefqne3e0XP+\nV+UWj7lUGVx2v6S2X/VL9bzU72d/TbuH+p9byrh1XnTy/tb9kDEOhB4aDiqPScYYWPl9pbCNXhj1\noEjV9xit4KqF+gOQP0cZ0/xOyJ2uJo3po9Xr2Icr8dYfRddwjIRDKtDJH4rg8oXYWdFCssVIZbOX\nMZOy6aTCnL74HAQrd1Ln9FHn8HO4zkXGwce55P5/qFy3dT9T7fKGbOjvHm+Lyg1PzlUG08HQsU/d\n/Aeo3QPn3aO+x858+Cs+KmlPKbh+Vj6WaE7r/monH5c10/juT2nKM2EfM7d/1w94lDduXyWUb8FZ\nX8aynT3nqR9vcNPyl++zpPN4f+CtuIqwVTW1dIuU7c9N7Z52I0UvOGpLAUhNHmCF5ih2u1IYymrq\ngV5WBQgH4egH7FnTXvJl+5/u5bzR0T571ufUd1WxVX33reUw8zNq3HfWqvnGaaY0DQt+p8rVbmPn\ni1B8EYw4HwwmOPQOb++p7hJtkLr3xyyckIVBJzBMX6rG6dL1hA+/i9Mb4liDm/Hv/ZDXPo7v71P3\nfZG5xWm8t7cWi6OS62f1Q0YpVdqKyYbv1f9jb5WDgzXtEREXjsskGI6woaSRzbv3s+fQrVy7cAHk\nz0aMHKDBaJhoq4o8ce6igR+clIPdaoK6NcCXem53+D0o3wwjz++5D2spw+kP0qizYzUpFSzDpv5X\n1DUBfRii+po3avRIr24PKeX70ZcvCyF+OMTKrh54GrgMqAC2CCHekFLu69DsCmBs9G8+yuM8f6hk\nOJWsPlhHkyvA2GYPk6rblwBJMhtp8QSoXPV78qderAazxCw1kM65HZLzlQdxzCIV7tpUAvvegAlX\nwfH1apBxVCkFpKVcTXQn3wCjLlJWekOCUjB3Rwchg0U9nB0JBwkuu59wJMLHZS34QxGSzAbMRj15\nS75JWsGErjdUuw82/57DtS4qm5Vles+Gd5h65V3tBQL8TvxvPYhh7EL0E69SA9yHT0HhfJhxq2pz\ndI1SDiOheLnCwZiyC1BS72K8001qUi/rqUmpJgEZ47pX+gdCWwGf3hTepqNw6F0qW7x4AmHGZiXC\njr+37z/+IQ2uAMJ9lPSqHSrn0edQyv2EJV1O5/j4VVYfULm7BaIBVv8Qro4+gu5G0BsJvfso7+xR\nVsfskd2E9g6CVKsKdTtaVsHMzAISOnp+AA4sU/9HLyIUkQRCEaxtnXBrJSTlDrv3fcdHah3JlFGz\ne2xjzR6F8VgNB6pb+6/wRsKAaJe/4QjYMpTh4vC7oDcpT2tnz/0g8TWUAip/FyDDZuT8wA6cviBJ\n5uhkr+W4ylOt3tEvhbe03smGfbVMK0iJ5WNjzQC/kz1VPYfaL51dwD83l5FqNWJLMFDZ7KXRFSDF\nYogrbtNRaQ2FJUJHFyX69Q6TrHBEEpYS/ZofsaZDQSCjXte+rmHHkP2Nv43eyIcwrpNXK5qXHFOU\nASSUN3vJT7UoT29DhyWV9r4KKQWEvc3oStYgomHPUkKtw0dGUgKBUIStx5vISlrGhJwkIlKiy5uh\nlPBjH8DCR9RvAGD5V3l1u7q3WSPSKGvy0NBBMWnz2P9xWys//2T3n/NJQ0rVj3anNIT8yuCZkAwb\nn+HfW+NDa2tavNQv+w5ZheNw+ELUOXyM+eBJpaQk5QyLuOF1P6ehvg6rSU9S9lSlaAfdcPkPIaGD\nMS/oBb8LEqOemn1vqD7HWQ0lKyF3Boy9XPX9oJ6fHf9QIf6zPgfZU8HTyKH9O2KhhUvveRJTxmhl\n8IiEmfjOt9lX7cAfDLPi+R9x6/df6V+f9o4qbxKKSIJN5aw62F574ZIJWWw73ozDG+Tq6XlUtnjZ\nfryZVk+A4OonMS64V41Tu1/GeWgt/mCYNJuJFk+QgKNTDYeAJ3Ytpy9EWZOHSZufU/Pgq7uZpkmp\nfss506itPAqALXNk3/fTDclRhbe5thz845VnsjvD+ZrHaaqvjlOMShvc6HUCfyjChcu/CuffCx//\nDW8wzMEaJ1OMiRhyp8KmZ9QB3d3L2UbpetYcrI/NbRLNVcyqqsK06V9kzb6O1p1vdBta3+IJ8J/t\nquBhyr7fMCEniR3lrfg79M/7q7sWWWrxBHhvrzKgrDzi5PqOO5uO4lr1M0IRSWrxbGT1LsT8u5QR\n58ByIlKybFc1wQ7yLJqYTfZVj4C3icz1v2PVgTpcvhAvvr0aIdYw/wv5jMpKVg6DU6Wovf9dypo8\n7JHF3Dpm4B5ejFYMel3XuhYdCfrU3BXUuFO+BebfBeFA+/gBhNc/BRJ0Re1GtNR01ae2NvbhQS7b\npCIop98KRfOV0yvogbReDE/VO1W60ZhLu+5zVIOMQEp+79c9S+hN4U0RQnR02xg6vpdSnujaEvOA\nI1LKowBCiH8C1wIdFd5rgb9KKSWwUQiRKoTIlVIOTSD9qSLkj03YDte6OFyrPIIjPvF/ZB78O1tL\nm/lg1QrmHdvM5mNNgJrAiTUfc9W0XD4qaST5453MG2Vnd0Ur4wJbMJarCqnNngDBcAR7GHSNh1l9\noI7Ew8+Sl/o3ijNs+IJhHL4QNa1e9lY5KD76DOfelKi8GGWbwFWD98B7sUldZ3b+7tvc+tir8Rsd\n1TSt/jUr99fFJrAFdgsVTV4aq46SEayBxiPUH9zAe/tqYdtfmZz3OmOyEympc1HoXk9axjj8W/6C\nyxfinb01LGh6nvRtL2JMzsI4/UbCQV9sQJiUl8y+KgcbN65n8WU9hHkB1O6FLc+BfTSc93+D72zD\nQapbfbR4gkxc82Pl7ezQgeGsIVKyBlG2ASFUDiTAlmNNmAw6xucksbuilTm1f2ZraTMAC/xPU2i3\n0ugO0HK8lFEjFyDMyR2uGeLdvTVxA50/FCEh5Me1+udUlB7GoBO4A+HY4uULZw2NT0nY2r2mr2yr\nYHxOErO3/FHd9743OFznoqTezaKsP7HmYB31Dj9T6m4nxWKkotlLVnICY5d8DTLGnrihoRtCH/w0\nNom6/epuOvEoaXmjgY+oqqoARnbfSEqCe16jYecKsi+8E+fGP9PqVcqmyxdCIvEFI7R4AhyJFslK\nNBu44PZC7LmjTkyxlxKdswo9EdKiYcXZyWYqm72UvP1rZpx/pQptays+Vb4JUkdAwVxl+e9MJALb\nn8dZp/KWd1W0sqtCKbg3XWjHgJqId8esEWnoBCqEGSipd1PZ7GXl/lpMBh1LZxcQlpLNx5oIhdvP\ncazBTV5q72sa7qlsZU9lKzfNbfcmL5mWy55KB8cb3TT983+w20y89nElhXYrs4rSONrgpiAtQsLO\nF9tP9M5DEHQT7ibHbV2HMOmJecmMy0ri3X01eANlpFiNeAJhUsxGUq1G6pz+2DPTMXy1osmLwxvk\naL2b0VnNVDR7mZyXTNE738M8+xYw2eJynbcfb+7xnufoDnWNXjlRavZAa4V6ppw1uDwezKPOw5A1\nXlXITspWE62moyoE/dgHKuT6om9B2K+Ma94maCkjVL4VfzCCbd5nOVLS/ZrLew8dIYNWlu+qAgl2\n2zHspeth6tKhuycpofkYHHyblR8fihkPLg0+RDgi2XS0kaLj/6uqz1/4DVj7JBEJ3kAY29xboWAe\nwUPv0+Dy0+QOUO/049v7DjMObqTB6afO6ecC42pqa2vZcryJvKO/ID/Nik4Q64uLJp+DKWuskkcX\n7a+u/Cmf5AFeiIbirn/2q1zw5V/1fB9+F7z7EFUt3jijDoDRoOPGm78AeTO56oMnVFTBJQ8yoWwj\nrHmR7ceb+ffKDeRs/ZgFYzNp9gRivzPzNT8l6bX78bV0mvLs+Af/3FIeV9F9Z3kLOakW5vvvRpcz\nCYuvDqYshYyx+N54gKMNLuw2Ewd9anI8pWgQE39AJOeDgHENK/G/tYrSBjfFZVsxTb0+Gl0RHWdD\nflZEjbF5E8+huWQL3kCYkmg/uvJAHbajj3K03h07d2TdMibnr+WVbUqR+9SY5egTs9Vz5GlUxvzp\nn4oXKBxU+efuOhhzmUppANUfBlyEXS7wV/kAACAASURBVA3obXao3EZ47+voF/9QTfQtaSqFQghl\nGAq0ySHBWaO+J3OKMnaGfEoGV60qwJc1CezFqs0JKnGRg2/H5jYALl8olvaRdPRPOH3tVd9NBh3B\nsER26gNbPUE2He05z3tEho1p+SkIQXt4PXCefi/yjXuJALrJ11P14QvtfdyuqPK2+SHsiSZcvlDc\nfGThxCzSJl9GwpSrVZ+Ukk/i0qdZvONlNq9+lbJGD1JKtj9/P7axmZjyp5B28d2D+5ACbpVaoTeB\nfVS8l7Ovz19KNu0rIRKRTEzqZ955Z/RGjNZkKloTcftD2NpSpII+FYaeOw259XkO1TrZFhsXylhY\ncYScZLMy7KQUgd5AvUv1ccaxC2On16VEV3r1dCqKFfJD2QZkzW5clQeod/rZeLSR0cd+w6yif9Dg\n8tPg8pOVZCYUiWA1GUgrnqmMf+fdQ+jQuxzd8g4gGVd8sXo2QgHY/CyRhkPUOvyYDDrSL/+GUuY9\njcq47mtV84zD78KUT0LC4KJBTjdE5wcntkOI3uJFpZTycyd0YSGWAoullHdG338WmC+lvLtDm+XA\nE1LK9dH3K4FvSil7WS8D5syZI7du7bXJKcXT2sBrP/li3LbZI9MYd8dziDe/xlu7a2jxBHo4uv9M\nzk9hb+WJFU+yJRhwB0LMG2lnT2UrnkAY5t7Jrde2eyTDq5/g36s2E5GSZIuRrLFzSHcdYtPRoa/y\nWzrpy9xveZNXtpWTZjNxxRXXwrjFKvyprQqmTgdS8uFTn6XFE2DB2EySF97XfVhbf/A288IP74i9\nvW5mPtZR50BKId4d/+7RONAXs0ekxTrHBWMzKPz8H9p3bnueF159vcsxSZMW4dy3ssv2a778GIkF\nQxRE6azlhR/Hh6KnWo1cMCYDR4fBeEp+Cnv6+H0tuPd5CjN7zqEbMFLywc8/TWWzF8vsT3H99Tf3\n3LR8Cy/+/kccHXUrD99xY7dt9j97Ox+X9bBkTi8IIbj5U59BTLlhwMcCrH3xSar3b4xVGm4zIrle\n/gpv7KjCmmDguhlqEAyGZcwDt3BiFtnzb0KM6SYsy+eA9x5hX7WDHZ3u6dzR6Ww73txjEZ7ZV3yO\n8a6tsXD8MpHH+o0bY/utJr169rthYm5yt56EzlwyISsWsXDLvCKqW5VyMGdkGg5fiEM13a85ao1O\nLs4dlU52cgLNniBv765mcl4yk/JSungnh4OFE7JAwKr9/V8r8earFqM7564hkyHyxj28v6+OBpcf\ns1HfZQmLC8ZmkJhgYP2RBvJTLUwvTGVneQstniDziu3YEgx8eKQh5tUEuHFOYezzG5udGDO+9kTK\ntCtZctMXe23TJ/uXwZH3Ia0Ymo8Rjkhc/hBv7hq4HfvKxVeyds27uHyDK77TVHgpd9/1le53ln5I\n08a/x5S2W+77OcLeQyWF3S9zYONb3RpBzr32LornLu72MPnWN3jxo8M9ynfz9//DR099hrJGDwvu\n+weFdlX7ofrvd8Wepb5Is5lihqaO3PKD/wx4eRYAPE0s+/mX4xQxgIvHZ5J32T2QMwWAo6ufZ+PK\n10k0G7jm4X8Tfv0e/rVlcM+qxaRn8eQcZfQ16DBd9gj6ZFVlOrTsflbvq4xVuE00G5hZlMbeqtb4\nSJATQCcEbTPljnPm6YWpTL7rz90f1E9q//HlLrmw3TG9MJXJeR2M4qMXETr0PmEp8Yci7KpoJd1m\noskT4HiDUt6nFqQwZcZ8hLcZFtwPQof71a/hDoTYXdFKrWNwRZIWXXYl2Rf10A9EwqpQWcDFy889\nHjfmdHGW9IWzhv0vPsjHZfHPVarVSItH/f4m5iYz8/zFKorRnApGi/JI2zKRZRt496Xf0RhVMhd+\n5dfk5BYMTIYo+5+9g4/Lmim+/TnO1R8Ak43Sd5/moyP9q9ycbDFy1UMvsfYPX2ff8WrOves3TC+M\n1qtorWT5b77Gish8fvNIezVuzyt3dwlJHywpViNXTMmhxROM9Wn9wZw/hRv+5wdDIsNwIITYJqWc\n05+2PXp4pZSfHTqRhh8hxJeIBtcXFQ1xsaQhxu1Vncz0wlQm5SYTikiM10Wtx5d9n1mt32BVp8Hs\n0knZ7Kxood7hJz/NEgsb7o0TUXaTzEauvnShsqa2VkLWJEau/Rkvvf8RbHmOyNVXotvzb7xH1sYU\nvrSx87ji0/eDwURTcxP87AtdznvO5NFkGrxsO94cZ9XsiWSLMeaNSbIYufv6SzCFZmDa+b80uwME\nSzdiKNuEmPU5wtv+gj8UwWJLQgY8sU5/+c4qxtjWMe/KQSq8/viJ+GsfVzK1/n0MOl2XjnggbOsw\nOVp3uIH5lXWMzs+CxhK2fNRVqQW6VXZbk8YMnbILYE7hvDEZcR15iyfI8k4T0s7KbprNRJrViMMb\noiE6wKx76raeBzm/E3RG5bWy2vuVI86Of1DZ7MWo1/Wq7AKI5FwAdP4elDGfI07ZTTQbYhPnCblJ\nVDR7cflCmI16clPM2BIMeIPKQyGl5J23/sPiQSq8FXs3xF6PyGj3AtoSlOfW4w/xwqYyFozNjDNg\nr9pfh8u5ky91p/DKMKGIpM7RdWmDDSXxxieLSY83EGZkho1mT4DCcbNg126l8F7yMNl7l8e170nZ\nhe7D5nprNzY7CWGykZGkJkJtnrae8PjVd7Jyfy3TC1OpiPZ96YkJGPWCxVNy+OBQPd5eZDxROvbH\n0wtTyUkxc7DGSSgcicnTmfUfreXCIVR4tx1viT1X3a3XuP5w+/N6sMYZF0raUx5pm7JbaxnFzSNC\nGPU6rNOvY+vbf+22vXvv29B6RXtdh0HgP/Aum442UtFc1mVfUbqVssZ2hbztd9oTb614K/ZarxPt\nS1X1k1uvvqLnnSPPx+6sJqvsFeocPlY+9yCXfuPFbpv6qvZ1UXZTrUZmFqWR24OyCyAufIAFDQ/j\nDYTZWhrvoRufk4ROJyhIs1DW6GHf4UMUzp8BQS+l0bGtr88H6FbZzR4xYXDKLoA5lTSbsYvCu+Zg\nPXm1P+KiLzyOSBtBbeVxPCQw/rMqRUF/9S/IOvjpbvunCTlJGA06dld0P2fxBsK82mHib695gsWf\n/zahlY+xfFd1rI8A5SHtGPEx4NvrxpgU6cExtLO8hQK3lxRb71EuPVKxNabsXjQ+E5NBFws37siE\n3CSl7C58VBXvi3o4DROvxgAkCMEFzcfBlknj0e34lj3NtMI0Mq94sMuzalv6G2xSMvNf/9ut4jOq\neBRz0oOUNXkoKVpKccMaPt5/GLvNRE6KmUmf+AIit5cCdjo9ZKm0t3NHp8ci3gA2vfMC8y+/pX9e\n8eqd1K1+Jm6O1faMO7yh2Ov91Q72v/wSet2/SbWasCXoafEECUck7g6/CzFm0aCVXYCMFBvQzMp9\nVZyLqivR+ZltY1xOUhcDrsMbpMXtR+eq4pjM5Yv5HRwBtgxMBh3Jjg7K7cEVrD3c9XdsTzTFGXI6\n6gNJ5q7PZRutniD/3Dxwg1NW4ZgBH3O6cipLl1YChR3eF0S3DbQNAFLKZ4FnQXl4h07MYcCvrOgV\nxUuZfPkS4jKszCnkXPNdPpX0OHpzUnsBpMU/5rLqnSpWX2/Cu+LRmKI5IsPGjMJUypvUMgbJFmPM\nw5ObamFCThKBUIQDNU5mFimL0qr9dZw7Op1DtU7SbCZGpFsJhSVmox6dAMvkK2FyNF81WhDLcNED\nTD94BzvLW9j090eZldgS5928ZOlXYqGW9jQ7t9z8WTavepVks5EJOSokQlzzUwiHuDjkJfLOQwRD\nkiZPgI9KGrEY9UzISaI4w4bDFyTx/C+iT8mHTb9ToRaXfhcsJiA7FibcNmG7sOX3cdVfO/Pxrh3M\nu3JwX1dk37Iu23oamEFZVcdlJ9HoDuDxh6Jh6YrsZDMLxmXw8lYVspWTaqEmqvhveuYuCh74LcG9\nb8c8LTOKUkmzmrpY85dMy6WkzkWzN8hN9/14cDfWE0YzI9OtfHSkf82zk81cctFCdHNuV4OdrxV5\n4E1efEUVStp9tIqpo/K6Hvjuw/iDEdYdaUAimV2URqrVSKs3RNKSxzAkdlKAw0EObl0FQMqUy/oW\nzJKG3WZid13XiTVA+MhqADKSErj8/r9ECx0dAlsm2DKYWbGFiLsR/bjLVUhV1XYovojZW//MS68v\nixmuBkzAHQulnZiXzMybHontEpc+yuhj98TC/tZ1M+CV17eofPzOBgIpefXjyrj8qu4Ym53E7BFp\nhCMSoylB5Rgl22HcFSrn3JKKSfa+HqDRoKPIbo3J2R2fnF0QC00EYhPdgjQLmKwYA+6eDu2RneXx\nBgoAu83E9TPz2VLaTDAcoaLZEwu7/sTkHNITTYQjklZvkBSrkbWHGhiXnUia1cSKPTWYjXouGJNO\nSb07ppRnJiUwr9jO+iMNtHriJxC6ix4g/fCznDc6HW8gjMXkiFvSpo2KDp7UE8bvjF1jTFZiLLx+\nqPjCvd9Fpw8zw5wC4QCFNSvjFIw2QmHJln89ztwvPT24C9XuY1dFa49Ggur8xdw6ZiuVLV7MRj32\nvNGI1nLqnX48gTB6nWDtoXqK0lU6iDtqoJoy50KmXf555OofKSNa0ENYSg7XumjxBJhRlBorSAWq\nWi1Tb0SXN6p3eacuZe7+Vby5q5o6hw8pZbeK4i6PGlfHZScxJT+ZBINezekzu6l30ZHELAqXPgEm\nG+PeeRAiIXzBCGajTlVWBzKia6vvK63mE/NnwN7XOBZVeK+7/mZE6ToqW7zYbSYsRj2BcISyRg8p\nFiPBiGTtwXoSjDoWT85hR3kLCQYds774eO9y9YZOx+jMxDjDRBtVLV5e/NlXufF/vos3rMNEiPE5\nUa+kTs+lt323PT83Sjgi0eVORdTuIRiK4PCFuPDOJ6l64/uU1Lu6Ne43VZey/Km7Y8ZwgCum5tLs\nDrDpWBMJRh0j7VasCQYyExMwj78EW864qGE1Q82rWsqQQS9Cp4f0saoeijVdpSs1HwdzMiTlqVoj\nKQWgM6jw6foDhLY+z7KdVXgDYXYdb2DBpMIuMvaLve3G4NxzPoXu2Bqunq7HlqBXBQcNFvw+N6Zx\ni2DiNe0pNN2F80bzONMnXMCisee0h3Z3hxDYbQncMKuAneUtlNS7uGBsBkWTz1N57jo9owD1dCxm\nsCpP/gWf5dbUl6l3+nlvXy0l6/6Nyx9h0TW9VIZ21UFrOTtf/xV7q1R/POembzNucjRU15yq5hkB\nN64V32P1gXqcPqXgNrr8NEa7RqNBh81sIN1mYkxmIlk3dXXADAT71Mtg9585Z/8P8Y/JjCskJoTA\nbjNx6cQswlJisqUxZ4SaI0oJuypa2FvlYPvBEgK+EMlG1ZfFMCSQajEy1lmBLxjGvOtvHP54HU2u\nAEkWIwvHZ2Fe+AB6qx3ee6Q9onv0QlW/p20Fh5Zy5NqfEghH0AlBo8tP9ojxeOuOxjzFBr2O88ek\nk3/D4/Dx31Ta1KEVeINhTHod+rGLiPjduI98iCVvIobzz55q6qdS4d0CjBVCFKOU2JuBWzu1eQO4\nO5rfOx9oPePzd4FIONpJ63r4+JNz0V/bTb5QUXu9Lsu1v2SB839w+kNMyk2GKZ9kQuU2NWkvmMuk\nXf+MVnWdovJP9CZGVO+A3Jnw5tf41NxCxCUPMsJVowaAlHy1pJCrVnX43eVeCsHE3CR2lrdw7NAe\njkU32xMTWLDkM5htyfHNp9zA/DGXqjyXjp2v3gD6JHSLnyAh4CLX08gn9/xH5REnZkPhXOKCYBc9\n2kWUSbnJcUpnR2VXCIGUkumFqSSbDWwra6HO373Vqz80W1TEwOS8ZCbmJfPytgra4ptuOG8yhoAD\nvU60jz2mRAi4yEsxAzAq04ZAKE9+wQyY8WlGl91JSZ2LyUsfYe6W38Q8MB//5euxJXQMeh1jx00m\nEg7BgTpSCiZw6ZgkZOYEzJOuYNbe11RVTv0wFIgadTGTyl9jX5UDnU5wwZgM8lItvL+/lgann8ys\nbJzNDfiCYbYHClg0+3Pt37ElFTHtU1x+YD3v7q3h2PInmXrPL+PPH3Cz9XhznBU0ztq8+wt88lt/\nJKGD0hte/QR7ogPghdf1I6zSZEOvE8geFKuyw2qdwh3TvsPlbb/3DkWhROE8YlNkc3Ks6qJh7h0k\nv7uC4zK7bxm6o2Y3vkCYBGsSM+/6Y/yzYUpi3kg7gVAkLvQUYPGUHFbsqWFSYA/y/e8hlvxMDXTR\nH16wuaJbZbejUeXmeUXoLKmQkIiutQIW/1jldxotUDhX/QHCnMzFE7LQQZdoE4BRGTamFSgjW9ug\nv3BCFqsO1KGP/l4SDPG/yzYvSVpGLggdQsCn5hbGwhzPGZVOfqqFV7ZXkJdq4fwxGfiCYVYeqGN0\npq2LkamjAgMwd6QyzFU0W1l7qB57oon08edBch56KbEfWAZz7+QS499h1CUw6mJuGBmtjjv+Smau\nfixmEGTE+WC0sMSi6jZ6g+GYcW/i+ElgugEOvIklI5O5pgom5ibR6g3GvBmZSQmxEMsTJhLBvUwV\nKGosWMStd9zO+Ne+TnmTh1GZiUSkMlTqhepjQuEIxxrd7ChrYUZRKiPTbXgCIZLMRkx6HRLlIa5o\n9uL2h5h+/mJ0iR1ytAwJWEx65o9K52i9i1ZvkLHZSTS7A1S1eFlRYaKfNYu7svn3HK1XM1KDXsfU\n/BTMRh0mg45DtS5mLzgHtm4lP9UCsz6vCvoBmXX7VYGtis3ckroGgHD+PLZ/uIKcFDNF134VhEAs\n+Wn7bQATl92rFOBz/kflYCblQNCLzth/j1zKpEUUV7/KsXo3eyodTC3olKLhqCJStpl6Urji8i9i\nbtoBU2+CD34MRef2fYE2w9WSn4GUmBsOQ+NhKDwHANuCr8COhyh07wauoPWQWgYrnJiLmLoUJlxF\n/uZnAQlF52HKmcoYv1Pl4ZWs5FPJ+yApGzHzs5xbvgnG9+LV7ie5KWaWzilAh4iNfc3uYGy1iWV/\n/AF2qwkJ8UvCZU1oL0QVLRCob1PiVj3GrLbaOyn5FMy9hrSDq6jceix2eH6aBbc/RIsnGFN2i9Kt\nnH/bDxG2TNJMNkbtex0sdvUMV21XY2Tn+YzJColZxJkuEjvkNHdc9SJjbPtrvRHyZ2HIm8mc1L+y\n7r3X2HkCCq/bqfq0kTl2dGMWwpiFJDUeUatjjLoIjDYS3PUqP38g9KbstrHgPszlm5lvP8J8ZzVM\nvwWKzhnEXfRC8QIoXkDmgbf4hG4Z7+ypoXX/KuhJ4Q14qF/2KNUtvpiyO3r8FMZNm6f2d1zq0mQj\ncenTXF23n9CGZzha744VV00snoux+DyVNtFdvYtBoC+Yg8nwF+ocfl7Z3m7IvWZGnvqNT7oO9r2G\nHgGXPKRSN4rORcgw6SV74NU/0FJxkKA3iCu5q6HNlmAgARdH693kHdnMlqj3eM5X/owttUMtiKt+\niajZreb2nWuIpBYirnmKBIBIhJxIEPQmrIff4xbjmwCIS7/T3udc8FX1f/wVdOwRdUDSzM7q2JnP\nKVN4pZQhIcTdwDuoZYn+JKXcK4T4cnT/74C3UEsSHUEtS3T7qZJ3KJERZZUOGU9gGRm9IZbPE+uo\nOq77OKLDQNs2uOdHK9oabYigW1V/7tiR6g19VmvTfeJHnNf0VbaWtucDXv71F9D1pHSZk7vfDmrQ\niQ48LHyo1+t2Rn/pd1gqv0uLJxiVJczskXYKL/ki1O+HkQtUwaqAi/01bpz9i7rsSsBDIBreWTrj\nAaZn1XGz7nWONXjITU/BfOVjql0krCpMpxSoidXan6jtU29EZ80ASxrGg2+patSGBOYX25k30o4o\nHAP7k2IT/44FPG44dyKG8++G/W9wy7xqRFomLLivXbYZtwzypvrB5OuZcXQNU/NTlCVy5uegYDaX\nyHvZU9nCmCvuJLL9b7z5cRnnzJjWdUKhN5Bx6Vdh77do9XVVwqSjKqbszhmZRqMrQCAcwReMxPJt\n3vzZl7jhOy/Hjtmw64CqXGq3x1UN7g2jQU8i3Xva6qpUcadrZw48zCkpORVPTc8en95oqFWD5Zq8\nO/lk54mJ3oBIH8UCoZYQcviCrD5QR7LFiP3ir5Bf+SMqm728uLmMJeFvkZKUpAZXvYGWtb+NnWZa\nQQq7KlpxY+bcUfaYsqYTwLl3q+fOVacGTF03k//0MeSlbAJUISt/KBLnrS2TWczWB1k6O/6zayt6\nBcC4xVzhWcaO8haqO6QvGC97BOr2wNY/odeJ9mPGL4GDb3LVtFwsJgPGqddj3Pca183Io97pZzfx\nCm/CuIXKWLfn5bjtBWkWbppbiF4ItWRbG2OjBc6u6BAR0XEt0CW/aH8thDLNjzgf6vZj0em51fii\nWvpDCDUZHbkgNuFIXHYvtugSE1aTHluCgXqnP77AyWBpPMyGoypcee6ipWCykTLrk6TU7FJGzaod\nyguVOQFj0Itx90tMyk1WhtAFD4DfgVVGlCHOaEWs+RHWjBGMM0W/z+6KUF39FKNXPMjozPiiW8t3\nVWNn8KHjDa4A4Ygk1Wrkyqm56juXETj0tlJy7TlqPMscH690ZEUr0CdepSpt58/BMOvTzJv96d4v\nePljYDDHV6oegLILwJjLGLXzPY7Vu1m+aS9TC85r39daAWt/wrEGD5lI0safD0RXF7jiyYEXtRMC\nMsepv7ZNljQsJj0JNaouSZt3v3hxtNyJ0Qzn3xN/HqNZKXAZY+KVutRBeiI7s+QXmIJutba1yQbe\nFtKAm62P8s/N5fgCYaoCXiz6XvrGzuuKL3xYeVatdvU5TLwKW/kmbp5XSESqvkuXUqDyMwHGL0H6\nWhHTOtVnmHRt++uCfqX2DRwhyC9Q2rm7tgSYOajTtKV11Z//vXZvbcbYeCV7oMpuf0ktalcgI5Hh\nXVlhwpWkT7gS6w/+n707j5OrLBM9/ntP7V3V+97ZOjshCSEkJBGSQAhBNgERGFQUhhlxroziiFx1\ndAZ1GIc7OqLMFb04IqDIgKCIiigkMCyRJQFkCxAInbXT+1rdtZ73/nFOOt3ppaq7a+1+vp9Pf7rq\n1Huq3uo+Vee82/Ncyiu9xYy4ECjcQ+j3/zhkSvesDR9n7QcTBMmrWoLzgu+zqL8juWVRE1VYy8xS\n35BrtPkf+iKBtYOyiXTutWYBOD1DvlfLKq0lRbObn+QdU1PrGT47LDbzA7D/Dxzu6iNsz+BYvWQe\ntSVDv4NRCmpPSFxfwzgahG/RWagFZ1r7TuOURgnPxEqpJ4H/AZ4GtmutUzZPS2v9CFajdvC2Hw26\nrYFRIkrkMdO+YFDJXbQnNN5euQ1fsD6YEznwPQHql6yhvvyNo1Ov0jHCmIi/HPdF/0lVfyfnPn6j\nFTVx9d9YjXZ7lIqNN0BvE/HGn+HtbmJPSy/zKsfZyfDmQ7Tba6Dmz6qDWcsxgPm7HoZNXz5aznBY\nqaKOOO+W4SeQ1YP6a7b8i3Uh4nDBOTfjaH+f5Y3fGBjFaqIU59l2Y7ruJNTeZ61UG5lUNBNH9wFr\nilOtdUJ3GbByVgnULIB5J3O5C4ylo4TEr1xMWcDN1t5j/uamSe8T1ohv13F/xaILN1n5fI87H8wY\n+olvce//vEooGufZW65gydwZlK3/FPvsEc/N/2uMaKnH8JXWUtFxmFjctNIKHKE1HT29vKtn8NHq\n8Xc8hXw1aBrp6ItS5h9fD3LXa1b+1nNWLRy5wNq/g2AL/qe+jd/jsBqE9RugZhk1dhRngD++8j5r\n55bhuvda6i79zsCF8Jal1RR6nLx6oAuzZC4+V5CZpT4KfS44/R+PjmSMFoAHrIYd9wzc9TgN1s4r\nx1DWemBvYRmQINDK4nMofedRNi2uHIh2C+BwOKzZHOf+h5U394g5H4CGpyjCHvWfvwmKZ8Gf/3PI\n37jA4+QD88qtHnWlrAiSO38KdSut0bwDL1i5g5d8aOz6HevYz6tS1gVU/alW47dktpX+ZqTy538P\nteu3XGo+jqFgd3MvDa1Bfv7Ag3z648dElR2nSOdBmrvDPO3dxMcW2imBFmw++n0zd8PQHdwF8Or9\nsOkfR46uec63re+dRN//Z3/LihLa3wHv/BEWnIl/77/S0jjBFUOR4MCxW/NXt0B99dGRqPr1Vpo9\nT+HY5zOHCzbfaI32JiMV0UW9RVSedg3s+heq3/8VMKjB293IE2+3oLXGdcyMhpQ1IJSBw47IT7iX\n3fbnfPXxo3x/ZIJhDP3b+qyZEcacU1my/5GBpQGDI7on5dj0Khu+gPH4162OutJ6WP8PQx7O5qW7\nYXfC9DY3TPg5eu01pusXTixidsqkOY3gET5/MYFQz/Dz8c472f/69iFLeGYffzLrEzV2jzjyXZ1O\nSrF2bjm1xT5ebGjnjOOqKFtxTN7rVVeNuKuv0Krb/m5rVkJP1ZphZSqLreuQt/cdZlEwwpt6Dpdd\n/u3U1T9D/+NclkzX86eADcDHgVuVUj3AU1rrG9JasylMBa3eenVsD+d4nfI5q4d1vPwVQ9PqjNfa\na6ypV7HQ+HvLU81XMnquPl8J+Eo4wddMh2rl9/f/Pz577fUjlx1N+x4au6yLtAU19nTHBZuttRNj\nXTAm+nI5duS7bC7L5tSwoMpK1VS5/GjIeioWZCcf4dprrMBSg4NeLPygNZLtLYb+TutCJDj62umo\nu4TanqYhI6H6tfsHpnDXLz/F6sE+0itvOFBbvsGW1r/jsTea2NsWZG/bO7DD+rppmXEGbl/yqV76\n8BHBQVNP2BpBOqLpdbr7YzgdxoSCtxT6fcxUrbT2hsfX4NV6YKrrmrmjnKCdHutvftZN1nKAeNQa\nscFaI6jslCqxuMmzdmCxS//wVd63e54rL/8hHHqJzf0/pqiuHFZ/jo3Ya/aSHS2wXw+AGauhsIb5\nWDMdPC4HZfXFsOY6K8dfnTXtlOd/ZKWYSZbDaUUOffo/rPueQjj1H2DbN60piTBw7Dt+ex2zy/3U\nFHlYUGV3UBz5v9WdCHWDPh/zGi4tzAAAIABJREFUTodw99FRwVRQCopGWIc++PFFH8T13lYorGUh\nh3hpbwcz9z4ITK7Be+iQ9VlZeNLGBCVtdSutXLSjHdfjmeLn9FjTgO2R8D5HEQW0E42buMbb0Rls\npd3OPrByXt3Q+nkCA9F9E0r3he0IjLJ6fG4HhaFB8QC0Jv7yzwZmL5zwye+m58ULq/F7nPSGQoQf\n+QqmqXnPswSve4T8ytm24q9YuW87bx/uwdR67LSByfCVwvnfs1JtlYyRazQbAlUU+lzU9rw24afo\nDkV5SS/krwpSM+0215UU+qlqP8hrB7tYOfvoDI6/PP/EwBTmJbVFLJ1RhPucz2armqNSW77OHK2Z\no7XV+TbWDMbB+7l8Vv7poDWgUVkz/FxSUW1tazm0h+LuEBXu2NBOATFpCRu8WuvdSqlOoNv++SAT\nnb8hAND2yG7cPcne54mm2UkFpbLf2E1SXbEPFJQ3PkMwfN34phj6SmkP2jk7B0+jTcO0EHXOzfhM\nk2U9jWNfXGeKt9j6GWzxOdZIs1LWRfBLd1u5D0dRWeCgo72NHXs7OLneulB9b8djA49vWTbydOLK\nC/6V8xz/xNa3mgfypNYUeznvE+MLPFFSUU3FnteHpS0x9z5HLG5SWDOxiO6zou/TAOxv7mRR9Tg+\nx9F+Wu0Ii0eC0YzqyAjKoI4xdfqXWbTnSRzG1iFpv4ak5lEKeg5TXeSB3n1Wg2XFxwZGYZLmr7JG\n2xZshp4meMtq8NYVe6G0zprKOGfQaNf6z1sN4B13WDMuBtl0XBUvNrSz5fhjGtwls60L2iOzXo58\np8xaO7TcGf/Mer559P7g6a7HKp4BjL00Iy2cHmvU2nDg+N3nKfS5xoxunazIbitQ25qF45h6n6Zp\na2UFBmWqm+ZjO5CS1BOKstNYzsfybVpdQRl+n5ednQEG5g2YMVp7rM9yTbGXxfPS1yCrKfLS1BUa\nGAGrmZ3DkVM3fJHzQjcTMzWlH0hBsg+lsnutMxqlKPI6Kemf4HqpeJT+aJy4wzc0gNEUVlUzg/f2\n7uNPrx442uDdu5037BkBi1afwcoLrs3d0cixzjtjcflwOw36w9YstSV1w8/F7sIKK7/1+z/HBJpK\nT5pERcVIEh5VSqm3gd8Bc7DmuC3TWp+Z7opNZTpmzd9XowWtEimlzvgaJ9r5zp58ede49o2YEIub\nqLL6NNRsBIZhXbDn6gWhUkenIXoK4QPXjtnLuahE4yTOjqeslQvRv/ySV+10Rud+7v+O3oPpL6f4\n3K9z8ep5fOxjf83HLjyfMz79HxQHCsZVXWfcGn050DF0JUZLvzXVLjxv9JQhY6q2RqPC4XFGau46\nQHd/lDd8qyb2ukW1cOJHmV/p52NrZ7N5ydAG5KazP2LdODLzY469vmj2Wmtd5Hic8dWj02YLq63R\n2OMvsp9vlGA81cutvNgnXGbdP/4i8BRSW+zlghV1+E4cYYra4GPKXQDnfgcWHTMy5CuxRniOdMBs\nvnF87yVTHE7r/Wy4ntICN7uitZjjTJUzRNt7HO4+ksYuhfmsJ6ggUEIM50BanHGJhQmG43QWLkpc\nNgd53W4UVs5gTBN2PzYww6Lq8v+b1tc+0ql2JNJ5bZF3rOLZVTKLwtP+ntJzvmZ1ik1hhXbnefNE\n8tm+8RA9oRhn+d5Oca1y1xynlWKo4YWHB7a1bL8bNBwqXcXqiz6bu43dyXD58bmPXu+PuLROGZT4\n3APnixXHJ4jwLsYtmRbX7cB64BJgCfA/SqmntNZ701qzKczos06S2jE9prFkXaCSWYtX8cq+rbz9\n7h7OW7c88T62Q91xQrhRJ12TxgpOXUem+zYf2ove8VOeeuJPhCJxKuafRElVglG4QBWc+++Tev2i\n6nnA9mGNjsZmK/Lw0lnlE3pez4zlwBO83zK+XNexHnvda8Uk19/ZU9yrn/0+p5kmL+/rZPNxVfhO\nsnNvBeyG8HgbuWM5EuRk/qbRyxjG0Ciw8zdZP7+9zro/c/japWEcI0zVNBxDA7blupLZxErnUdu2\nm9beMFUTbaD0dw7MMCn0Zn8Ka0GgmCKC9I6S63FM/R1orakpzc9GUI0fZqtmtj63kwvNrYQ7Gwfy\ntS6b4PdIslwONZDKDGDLKROOk50ZqVxOkMMclQvh8Eu81xIc/2c8UEksrtlRcSGTj5udH4y11+B9\n4QY2RHdY6XfC7QMpFzeffkaCvfOYYXAkftsBXTmQwWOIqiWsnF3C83vaKPA42bAhxz/jeShhV4rW\n+j+01h8GNgN/AW4C9qS7YlNZr2n3M8gIb8YUnmDlFG5pHjGN86j6I1HadSELZkxizfN0tuWbBLxO\nFvbu4Nmnt9LUFWJBVYCz/vqfEu+bAg6X1UjY29Q6ZHt/20GadOmQdUTjUVZoTedsbRs58fxo2l7f\nCsD8+voJve4whosZJT4rsvGF3z26vrFuJWz833bwqRziHt8IfT6rix3AT2gg6viEKOgLx/hN8Rh5\nKzOosm83AC373hr3vsE267u3oiZFkYIzbE6Z1VAPb/t3nnnljYGo5QvHs6Rhok64nLkVRzsKPNVZ\nDFglBlQ7rAB7Te0d4943Fu5Da024oDZx4amibC4L7SCRe/54G3vu/wqxuOZA0UpWrjolwc75raDQ\nmmU4U7WMHDdEKWrXXcpFp63lrL//AT5P9js4p5pkpjT/H6XUs8BO4CTgm1gjvWKCYrEY/XisSKIi\nM/xVFLgdzO54bly7BUMRTAxqR+qRE4l5i1lWZ03F3NcWxOtycPJn787Yy5cWWOtkvXrolLNQsIse\nCqx1rhPgdFono3i4P0HJodoPW0FvFtZPbO3wMAvs1SXrrh0ajEip3J4aPw14/VZDaH/bRHOiQbDN\nymu6bE5VSuo0Wb66pQC4473j3rcvbl1uVJSldzQ0XTxzVuFzO4jFTfa1HV0iMefsz42xV4rM+QAn\nzixhRqmVn1rkBmeR/bnsHZ6rPJGukDVaP7uuJpVVynkVy61sE688t43n7DgUl1yagrXeOc7jts7P\n7+oxZrYtOBNOuwH8+fkdmeuSGWJ8GbhVaz2+oTExKtM0iWNMfJqbGD93gR1EpgfT1BhJdjaEwyFM\nVE5MJ8xX8xYt43D3Dhq7QpRuuX5CUZEnylVkpXs41Hjo6MZoiN5wDNNwTbwuvlK8bgd9nYeT3yce\npaXXanivrE9RGorKRdmJ4D1eH/h7K8XNNBKdtwXe+Mm4O0UGa2+1jq+ZtbkxCuSatwF4mPfaxx+M\nK3LgZQBK/BPrZMq6ZZfwwYYd/PGNw/RH4pxcX0ZVkYfihWnK9XoMVTKL0xYBi8/NyOuJxDyLNsNT\nz7KndfzZOvuarYj2hf7pM+sFoHrO0LWpy87/LPPmjpEib4qYF4jyDuCuzs8YBlNBMlGa/1spVayU\nOgnwDtq+Pa01m8L6whE04JaQ4xlV6vfQ1BXivZbepKeh+SMtODApKZAG74St/zynVP4B2t+HdePM\nGT1JLrf1leV1DFrDu287wXCM6slcZ7gL8budLOl5Fvh0cvv0tdHcHeZR82Q+Np5I4VPBZNcs56Fi\nn/Wd8f6hJmBiFzkd9ijQrPIMTJtNguGwIoaX6s5x76t6rcZ7gTtF+eczzROgYPEZXOT6HzjuXJSv\nbOJRWydi4xchEpzygaDyScBrfY8XmeOfxdEasjpbp9vsMaNyISfNKSUYjrHqym8nnyovz5X53Wxe\nUk1xeVviwiItEl51KaWuBq7HyvPwGnAy8BxwelprNpV1WWt/PC5p8GZSdcDNW8ArDS1JN3hbw05i\nmLimYuTATFqcnbAcylNIgdvBoY6jUzDNrkOYpubdmkmMlPhKMRR4iCUue0THXmKmxlM8vaawTVfF\nZdb/2TeJvo3WriAdBFhTkSOjQN5iAl4nO1vHP2rdGXHQg48T8nlm07KLUcsuzt7rS2M3pyhfGW6n\nwRtt449aXhA8QDMlrC3Lkc92pngKOW7JCVC9dNo0dgE445+o3vYvsPbqbNdk2krmKv4fgNVAg9Z6\nA7AKkC6KSXDqGA7MgQi2IjNK7b93pGN/gpKDaJMOAklPgRY5xnASjpm44kcv0Jsbrf//7Fn1E39e\nhxNfcRVtMXfSaWcioSCmqZk3LwdzSoqUc7rslCXjDGw2WHHbK8QxqJtAztu0cLiImRo1genpTjNE\ng66hPCDnPTFFONxE45oyNf417U0hhZM4Huc07Exf/3lYuCXbtcgsf4W1/Kg0ffm6xdiS+aSFtNb9\nAEopt9b6DSCFuS6mHx2LEMSLS6Y0Z5R7zVUAHDicfIAJf7yTQl+erjkT4PRQFnDjNY82eDtCmn48\nLJ85ev7gZJhAn/bSE05ulLdn7ysAVBbnxvRUkV7KTjvnMie4htc0icRMNAqfK0emATs8FHqcqL7x\n93n3xBz4iEg8BDF1uP2U+900doy/wVsSaaFRl1OTzzMehMgjybS4GpVSJcBvgT8qpR4EDqS3WlNb\nezDCIV0ha3gzzFkyEwB3X/INXq0hoCLpqpJIN08RDqXoaTk6qh9tb+CgrmBexQjJ38ehoKyOWaqZ\n9mByx0e7YaUMKi3PjYi7Is38FQS8TooiLRPbv7OBtmCEvd7jMxrobUxON8U+F0a8P+mZDUeEoyaN\nugzvdBzRElOTy0fUNKmKN41719Z+Ey8RnHIdKERGjLq6SCn1CPAZrfUF9qZ/UkptBoqB32eiclOV\nx6mIaQe+fA3eka+8JbidBh0hM7nyWtMWjNBsSBqIvOVwogGX52gvemtI4SRGbcnketZdZoR+PHT2\nRYDEa+t6m98njIvFubIeU6SXO4ChFLvbohPbv3MfvaEYLYVjpLHIAoehWKoa6OqPDiwTSYbScdxO\nh1zgi6lDKUoK3DQ1j/9azquiHNRybSFEpox15vkp8Cel1D8qpVwAWuutWutfaa2nV36JFNNmDI8k\nlc48w0mxz8XB9p7kyptxvE6DUDxHRlfEhLj9ZbhDrQP3vSrGYV2Gxzm5Did/aRV+QrR0J5eSItTd\nShQns6ZbkJLpShnETE3AM7EGnmlqTK0pqqpPbb0mye9x4iTO/o7xpWLpCvZjOKdZdHIx5WlvGYYy\nicaT7EgHiIbo6o8yp0iuLYTIlFHPxFrrXwInYY3o7lBKfVEp9YUjPxmr4RTkiPQiY7tZYDhwOw0q\ndRtaJzEdL9KDqaG+RC7S8pmK9qGAUDQOpklXTy/l/sn/Tx1ea0p0XzC5C38jFqJT+6nI1zykYnyU\nQYnPRXcwNKHdQ+3WyqHq0slNvU+1wqISAPa2jmPdYiSI22lQaIwjqrkQeaBId7NSvcuhznGs1Y9H\nUErxXiSDaa2EmOYSdT1HgCDgAQqP+REToTVdoRjxZBpcIrWUFfylXjUlF2goFqazL0KvS6Yd5TNX\n+RwUmkjchFgIl8OgOz75RmdRRS0ALd1JXPhH+ugN9uE3ohLxe7pQiqipCYYnNqW5zW4n15bm1unW\nUV4PQG9wHA3eeJS4qVFFtemplBBZUlpgzdZ7saEj+Z3iUfoiMeZXl6SpVkKIY421hvds4LvAw8BJ\nWuvxzV8ag1KqDLgPqAcagMu01h3HlJkF3A1UAxq4XWv9/VTVIWtMKwx92CVfdNlQ4A+g6OJQZz9F\nNQmmlfe143QYdIXjmamcSAvldFGtOugJxSgyuujoi1BdUTzp5y10WQ3XeF9n4sKd++gJRWnyLpn0\n64r8Uex1UtvTmrjgCPpDYXrwcVxNbjV4C2evAJ7gYNM43pc2aQ9GMH2yfldMLaXFRUArfS17gZnJ\n7RTqJBoz6Y9IQEwhMmWss89XgUu11l9OZWPX9mVgq9Z6IbDVvn+sGHC91vp4YB1wrVLq+BTXI/N0\nHNPUlAYkFH02GNVLKaSfw0lOP9JaU1cjoxL5zBnvJ4bDCi5lRnEaigOxyTd43cU1KKVo6kzi6zHY\nTH/UZG/Bskm/rsgfDocBZsyaTj9OPb09aIyci2rs91rnrq6OcUSf1hqPywGGLOYRU0uBPU3f8f62\n5HfSGq2hqrouTbUSQhxrrDW8G+ycu+lwIXCXffsu4KIRXr9Ra/2SfbsH2AXkVrjKiTBjVhoTlVsX\nMdNFgdeKKtrVm3g6njZjRGImhlPWXOYzb8UcDDT9kTiEuumPxFlQk4IZFoYDrTU6ljiGnw73orWm\nqLR88q8r8obhCeAhQk9o/GtX3eF2HMSpK/GloWaTEKgEoK8z+fRuBJvRWlNVlGPvRYhJMsrqAejp\nDSa9T6SvE1NrHBLETYiMyVarq1pr3WjfPow1bXlUSql6YCXwfHqrlQGRIB6XQTw2wVQVYlL81fMA\naGzrSli2r7vN+i1xVvKaMlwE6GdfW5BY1GqcdqdiJllfOyUFLupank5YtH/PdgBmVEmDdzqJB2op\nUz3JR4YfpK03RK/24XHlWOeor4wCj5Pi+DjWLIa66I/EiXomP7NCiJyy+m/wuh3siyS/9CDy/nMA\nFMiEByEyJm1nUqXU40qp10f4uXBwOW2Fyx01gpNSKgA8CHxea909RrlrlFI7lFI7WlrGMdUq08w4\npoaicpkmmw3FXqtH1REe9VAaELM7Jeqry9JaJ5FeZT5rra1TxQnba6Zm19VM/okrFhGJazpU4tHi\nLqfV0F0gQUqmlTK/hwLCvPLHO8e9b6HZTRgXlYEcm2HiLaYi4MHRtTfpXeJxq9ewJZY4X7UQecVb\nRIHbQUXscNK7dHus67+C2kXpqpUQ4hhpm0+htT5ztMeUUk1KqVqtdaNSqhYYcW6Unf/3QeAerfWv\nErze7cDtAKtXr87dEMjaxDQ1Dod07WWDu7gGQyneP5y4U6S33x4GdMlFWj5TAWsCSVNnkJ7IfgC0\nck/+ib3FVATcPN2SeA1vsC9EBwHmuuVzP53UeqwZBYWHXxj3vrFwH92qCqVyLKq3UigFc9Vhuvqi\nFBckzikfj1trmCUqrZiKyv0eanoPJF0+1vouAA6HTGkWIlOyNVfqYeBK+/aVwG+OLaCss/xPgF1a\n6+9msG7ppeOEonFiOsemqU0XDhcaiAYTT2mOdx6wd0l8QSdyl99nNW4j4TD9ptXgLCtPQaopw0Es\nrpMKxBOOmRTSz6zSgsm/rsgbvnALXreDaHSc6yJMk1DUmg2UiyoD1mfq7cOJZ8oARGLW+3c6pcNH\nTD2mnWYymEy6Q6A1bGCimF0unelCZEq2Wl03A1uUUruBM+37KKXqlFKP2GVOBT4BnKGUesX+OTc7\n1U2deJ+17snjzLFe++nCW4LP7aCxK3GU5pi2Ls5qS+SklM8K7M+aK9ZLsGU/GkWJPwUjvEpRWuBm\ntXorYdHuUJSDuoICj1zwTzflfvfABXHSzCiGUoQLcjOKa5HP6gTs7W5Pqnx3t7WGuS9ipq1OQmSL\nqjoOjaKrP7nYLK5QB4d0BSUFKTgPCSGSkpUGr9a6TWu9WWu9UGt9pta63d5+SGt9rn37Ga210lqf\noLU+0f55ZOxnzn0x+3xfXFKa3YpMVw4nhR4nS2K7Ehbtb91LDz4MGYzPaypQDQrePdRKFAOFptCb\nmlF7pazUVYl69otCjURxUlmYY+sxRXot2EKZ3bmS7MUwAGactmAEryc3L4g9vgAAh1uSy8Ub77dy\nVS+olfOemIKUQR8e2nqTi4bY09GEV4WpKpLzgRCZIpfyGRaxg+ZIqpss8RRRFnAzl0Z6EzRSnLEg\nITxUFUrO5LxmODFQlKog3R0tNFNCeSpGeIH2oiVEcNKZoDHTFDLwEMXtkK/caeW483A4rWPtnSSn\n/wIQ6cXtMDBzNJq/86RPABDsT5ySC6A9bB33LlduNuCFmIzCslr8hAhGkpvSbEZDNOpyilLU8SqE\nSEyuvjKss89q8IbjWa7IdKUUPpc1rXRf29jBhoIRa611wCOBJfKatxi/x8metj7cZggPUWqKU9OJ\n4S8sJoyLSGzsqZoeQ9Ooy/C6ZErztKIUJV5rSr1pB6pJSjxCdyhKaWVuTmn2eqwL9a6+UFLldTxG\nGBd++S4VU5DLtD4H+1uT6NSKRYjFNQ5ker8QmSQN3gw7kp5hdnkgyzWZvqK1qwB4+/DYgauisTgH\ndQXFPumFzWuGE7fToC8coauzg2ZKcKVqpFUZODA51DnGmnCtccaCBHwyujUdeZ3WsdbZOb68tWho\nT0W+6DRwORy4nAadrYeSKh+PxzExKPPLd6mYespc1gfVHQ8mLmzGiMZN4qXz01wrIcRg0uDNsFhX\nIwBOp5z4s6W2rBiA95sSRGrWJhgOfJJKJr8ZBi6HIhBphWg/rhT2rFcFnBQQpuHNF0cvZMbp7Ivi\nVDkaclekVXzuJgB69DhmFcSjaGBBTY7mAC8oQ2uNSjLAge/QdnyEU9fRJEQOcZTMAGDfoSRy8Zox\nesMx4pKpQ4iMkk9chnVErMZTXHK7Zk1pwAdAvP39Mcv19XYllXJG5DhvCUU+F+uMXfSFw/R5qlL2\n1LMc1qhd+Z6HRi+kTVwOxcGIpCSajgrqlgAQ18lH5g9Ho2itMXP1PGE4KSlw09KUxAU+cCRItaxZ\nFFNR8QzrM36wI3FOdmJhTA3FfokNIkQmSYM3w7RpjS7VleXohcw04KhcgNOh6GsbI1G8GcflUDjj\nidMXiRynFCU+Fx6ihCJxVhSOI3hQAoa/HAAXYyzK13FMrZldUZiy1xX5w2Wv297T3JP0Pr29Vllt\n5GgD0R3A6TAoizUnVVzbLd5Cr6zhFVOQUiilmN/+VOKyvU2Eo3FcLvksCJFJ0uDNsOZuqwfQ7ZQv\nu6wpX0CB2zn2mrp4lFhc4yqdlbl6ibQZnA6opeTEFD6zosjnYn/PGNOVY2E6glEcDvnMT0due/lK\nY2cS6/tskR4rv+2MiuK01GnSnG48TgMNROOJlwj0ag/v6hk4DMk/L6YgZeB1GcyM709Y1IxYnegF\n5TPSXSshxCDS4M0wpz0SVCGpbrLH6cXlMKgIj3FyMqO090WIapnSPBUMDjy2ZGkqG7zgMBTB8BjR\nhSJBXA5FXzg3U8yINNMaj8tBWc9bSe/S2Wel+4kauTsN3ltSw0zVQmtv4tREvaEYLboYpaTBK6am\n8oAbUyeO09C3bycAhjdHO7OEmKKkwZthrr4WAArcMtqTNYaDIq+TCC5C0VGmooa68ToN3Ibkj5oS\nTv8Kl508iy3HV3P6qqWpe15XAYVeJ2VqjNG7WAgTKK+WHv1pyVeC3+NgUd8r0LwrqV2cfU0A1Ffm\n7tIXl9tHgH6auxM3eN2GxuvO0enZQkyawlAGXX2JOzVD+/8CQFVZUborJYQYRBq8GdbQq9AonBKt\nMqs8JdUsVvv5y/7OUUpoTA3+0tqM1kukSWENzgtvpfJjP0KlMhDZ8RfgdzvRWtMfGa3zpItQJI5T\nAqBNT8pBiT3DILr9h0nt0twHYVw5HdXY6w+gURwcKyWXraunV/KZi6mrYiFx0+SwqkxYtLXoeACK\nCmWEV4hMyt2z6RQV8LroRaYzZ9tMtzUi9/K+UdbxapPu/ihGkmk3xDTl9OC286x29Y/cux8zrWlu\nzfHcnZ4q0sgwKC2wcjD/7tVDmEmsea3sfh0PUaqLcvdc4a+eh5sYxEJjF+zvwO00ODH2l8xUTIhM\nUwqzdB59OnGnTrD1AN34mVUm5wMhMkmu5jNs0Yr1zF9/abarMe2VzV8FQMueV0YuYMYxlKI3IrlT\nxdhUgRWp+XD3yBf+sZjVEJ5fLT3605KrgJpiq+HaH4nTHkzQQAQ6+qKYqJweFXV7rAv2fQcPjl0w\n1E3c1EPW0Qsx1WhloLQmGI6NWa5Xe4ijqCvxZahmQgiQBm/GrVy1ljPP/nC2qzHtOeduAAUth/aO\nXCDSiwbqKwMZrZfIP9HqE4jiGHU9eLzbylXqlCjN05PTM6Sx19iZIFen1mit2aXn4M/hBm9JtR3B\nPpog+rQ26eyL8JeCdemvlBBZ4nU5KVbBUWf6HOHu3EOf9uZ0Z5YQU5E0eMX0VDKbgMfJ+uizIz5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OEVQgghhBBCCCHSLVtTmoUQQgghhBBCiLSSBm+GKaXOVkq9rZR6Vyn15WzXR+QupdQspdQT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DuZ8vdITXF2Do3nzTOqKTs3Uu02WJ+jen14im+aF1BHjxkGPG+Hll4eZq7wFVUjhe7T0g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\nIiIimpP+P2NN9Nal9mWsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b493d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,16))\n",
    "\n",
    "plt.subplot(511)\n",
    "plt.step(range(len(measurements[0])),x0-mx[0], label='$x$')\n",
    "plt.step(range(len(measurements[0])),x1-my[0], label='$y$')\n",
    "\n",
    "plt.title('Extended Kalman Filter State Estimates (State Vector $x$)')\n",
    "plt.legend(loc='best')\n",
    "plt.ylabel('Position (relative to start) [m]')\n",
    "\n",
    "plt.subplot(512)\n",
    "plt.step(range(len(measurements[0])),x2, label='$\\psi$')\n",
    "plt.step(range(len(measurements[0])),(course/180.0*np.pi+np.pi)%(2.0*np.pi) - np.pi, label='$\\psi$ (from GPS as reference)')\n",
    "plt.ylabel('Course')\n",
    "plt.legend(loc='best')\n",
    "           \n",
    "plt.subplot(513)\n",
    "plt.step(range(len(measurements[0])),x3, label='$v$')\n",
    "plt.step(range(len(measurements[0])),speed/3.6, label='$v$ (from GPS as reference)', alpha=0.6)\n",
    "plt.ylabel('Velocity')\n",
    "plt.ylim([0, 30])\n",
    "plt.legend(loc='best')\n",
    "\n",
    "plt.subplot(514)\n",
    "plt.step(range(len(measurements[0])),x4, label='$\\dot \\psi$')\n",
    "plt.step(range(len(measurements[0])),yawrate/180.0*np.pi, label='$\\dot \\psi$ (from IMU as reference)', alpha=0.6)\n",
    "plt.ylabel('Yaw Rate')\n",
    "plt.ylim([-0.6, 0.6])\n",
    "plt.legend(loc='best')\n",
    "\n",
    "plt.subplot(515)\n",
    "plt.step(range(len(measurements[0])),x5, label='$a$')\n",
    "plt.step(range(len(measurements[0])),ax, label='$a$ (from IMU as reference)', alpha=0.6)\n",
    "plt.ylabel('Acceleration')\n",
    "#plt.ylim([-0.6, 0.6])\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('Filter Step')\n",
    "\n",
    "plt.savefig('Extended-Kalman-Filter-CTRA-State-Estimates.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Position x/y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#%pylab --no-import-all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAo4AAAAUBAMAAADxQqHfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nXnPtxSbTayiZ/2MtW8J/Aat4iYISw9a0AAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left ( -41.8453628724, \\quad 635.263935784, \\quad -29.3921077057, \\quad 361.534304832\\right )$$"
      ],
      "text/plain": [
       "(-41.8453628724, 635.263935784, -29.3921077057, 361.534304832)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JrFmzBhcXFzZt2gTA6tWr6d69Ow4ODkydOpVOnToBsH//fn766SeWL19Oz549iYiIoEOH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hwPb9xRN06Y7Fe70cI3lA65+VmndHyrQxk7Vylr/8+ycrMu+vvWaNRa4+68VcOHD1f37t0VFBR0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\nAACgMiDYwidkn0rT0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Zyb6zR0vQnS94MbSncwYwsAAAAgcHCNra/5xz/0emamjp9z2Eh6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b425790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "# EKF State\n",
    "plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
    "plt.plot(x0,x1, label='EKF Position', c='k', lw=5)\n",
    "\n",
    "# Measurements\n",
    "plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', marker='+')\n",
    "#cbar=plt.colorbar(ticks=np.arange(20))\n",
    "#cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
    "#cbar.ax.set_xlabel(u'm')\n",
    "\n",
    "# Start/Goal\n",
    "plt.scatter(x0[0],x1[0], s=60, label='Start', c='g')\n",
    "plt.scatter(x0[-1],x1[-1], s=60, label='Goal', c='r')\n",
    "\n",
    "plt.xlabel('X [m]')\n",
    "plt.ylabel('Y [m]')\n",
    "plt.title('Position')\n",
    "plt.legend(loc='best')\n",
    "plt.axis('equal')\n",
    "#plt.tight_layout()\n",
    "\n",
    "#plt.savefig('Extended-Kalman-Filter-CTRA-Position.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Detailed View"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x116aa1450>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Td0zn3ysbDeU1SjdiZts73uxBCGGBvZ093et2Z//L+1nebTlNKjbJsf2FW/v5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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a7b7a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,9))\n",
    "\n",
    "plt.subplot(221)\n",
    "# EKF State\n",
    "#plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
    "plt.plot(x0,x1, label='EKF Position', c='g', lw=5)\n",
    "\n",
    "# Measurements\n",
    "plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', alpha=0.5, marker='+')\n",
    "#cbar=plt.colorbar(ticks=np.arange(20))\n",
    "#cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
    "#cbar.ax.set_xlabel(u'm')\n",
    "\n",
    "plt.xlabel('X [m]')\n",
    "plt.xlim(70, 130)\n",
    "plt.ylabel('Y [m]')\n",
    "plt.ylim(140, 200)\n",
    "plt.title('Position')\n",
    "plt.legend(loc='best')\n",
    "\n",
    "\n",
    "plt.subplot(222)\n",
    "\n",
    "# EKF State\n",
    "#plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
    "plt.plot(x0,x1, label='EKF Position', c='g', lw=5)\n",
    "\n",
    "# Measurements\n",
    "plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', alpha=0.5, marker='+')\n",
    "#cbar=plt.colorbar(ticks=np.arange(20))\n",
    "#cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
    "#cbar.ax.set_xlabel(u'm')\n",
    "\n",
    "plt.xlabel('X [m]')\n",
    "plt.xlim(160, 260)\n",
    "plt.ylabel('Y [m]')\n",
    "plt.ylim(110, 160)\n",
    "plt.title('Position')\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, complicated analytic calculation of the Jacobian Matrices, but it works pretty well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Write Google Earth KML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convert back from Meters to Lat/Lon (WGS84)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "latekf = latitude[0] + np.divide(x1,arc)\n",
    "lonekf = longitude[0]+ np.divide(x0,np.multiply(arc,np.cos(latitude*np.pi/180.0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create Data for KML Path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coordinates and timestamps to be used to locate the car model in time and space\n",
    "The value can be expressed as yyyy-mm-ddThh:mm:sszzzzzz, where T is the separator between the date and the time, and the time zone is either Z (for UTC) or zzzzzz, which represents ±hh:mm in relation to UTC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import datetime\n",
    "car={}\n",
    "car['when']=[]\n",
    "car['coord']=[]\n",
    "car['gps']=[]\n",
    "for i in range(len(millis)):\n",
    "    d=datetime.datetime.fromtimestamp(millis[i]/1000.0)\n",
    "    car[\"when\"].append(d.strftime(\"%Y-%m-%dT%H:%M:%SZ\"))\n",
    "    car[\"coord\"].append((lonekf[i], latekf[i], 0))\n",
    "    car[\"gps\"].append((longitude[i], latitude[i], 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from simplekml import Kml, Model, AltitudeMode, Orientation, Scale, Style, Color"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# The model path and scale variables\n",
    "car_dae = r'https://raw.githubusercontent.com/balzer82/Kalman/master/car-model.dae'\n",
    "car_scale = 1.0\n",
    "\n",
    "# Create the KML document\n",
    "kml = Kml(name=d.strftime(\"%Y-%m-%d %H:%M\"), open=1)\n",
    "\n",
    "# Create the model\n",
    "model_car = Model(altitudemode=AltitudeMode.clamptoground,\n",
    "                            orientation=Orientation(heading=75.0),\n",
    "                            scale=Scale(x=car_scale, y=car_scale, z=car_scale))\n",
    "\n",
    "# Create the track\n",
    "trk = kml.newgxtrack(name=\"EKF\", altitudemode=AltitudeMode.clamptoground,\n",
    "                     description=\"State Estimation from Extended Kalman Filter with CTRA Model\")\n",
    "\n",
    "# Attach the model to the track\n",
    "trk.model = model_car\n",
    "trk.model.link.href = car_dae\n",
    "\n",
    "# Add all the information to the track\n",
    "trk.newwhen(car[\"when\"])\n",
    "trk.newgxcoord(car[\"coord\"])\n",
    "\n",
    "# Style of the Track\n",
    "trk.iconstyle.icon.href = \"\"\n",
    "trk.labelstyle.scale = 1\n",
    "trk.linestyle.width = 4\n",
    "trk.linestyle.color = '7fff0000'\n",
    "\n",
    "# Add GPS measurement marker\n",
    "fol = kml.newfolder(name=\"GPS Measurements\")\n",
    "sharedstyle = Style()\n",
    "sharedstyle.iconstyle.icon.href = 'http://maps.google.com/mapfiles/kml/shapes/placemark_circle.png'\n",
    "\n",
    "for m in range(len(latitude)):\n",
    "    if GPS[m]:\n",
    "        pnt = fol.newpoint(coords = [(longitude[m],latitude[m])])\n",
    "        pnt.style = sharedstyle\n",
    "\n",
    "# Saving\n",
    "kml.savekmz(\"Extended-Kalman-Filter-CTRA.kmz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exported KMZ File for Google Earth\n"
     ]
    }
   ],
   "source": [
    "print('Exported KMZ File for Google Earth')"
   ]
  }
 ],
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   "file_extension": ".py",
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